

/ .'^:^ "^^o 




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" «•. 







THE PLANET JUPITER. 

A§ geeii with, the 26-inch telescope at Washington, 1875, June 2i. 



AMERiCAIf SCIEKCE SERIES, BRIEFER COURSE. 



ASTEONOMT 



SIMON NEWCOMB, LL.D. 

f:XTPERIXTENDEXT AMERICA:^ EPHEMERIS AND NAUTICAL ALMANAC 
AND 

EDWARD S. HOLDEN, M.A. 

DIRECTOR OF THE WASHBURN OBSERVATORY 



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NEW YORK 
HENRY HOLT AND COMPANY 

1883 



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Copyright, 1883 

BY 

Henry Holt & Co„ 



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PREFACE. 



The present treatise is a condensed edition of the Astronomy of 
the American Science Series. The boolv has not been shortened by 
leaving out anything that was essential, but by omitting some of the 
details of practical astronomy, thus giving to the descriptive por- 
tions a greater relative extension. 

The most marked feature of this condensation is, perhaps, the 
omission of most of the mathematical formulae of the larger treatise. 
The present work requires for i*^s understanding only a fair acquaint- 
ance with the principles of algebra and geometry and a slight 
knowledge of elementary physics. The space which has been gained 
by these omissions has been utilized in giving a fuller discussion of 
the more elementary parts of the subject, and in treatmg the funda- 
mental principles from various points of view. 

A familiar and secure knowledge of these is essential to the 
students' real progress. The full index makes the work of value as 
a reference-book to a student who has studied it and put it aside. 

As in the larger work, the matter is given in two sizes of type. It 
will be found that the larger type contains a course practically com- 
plete in itself, and that the matter of the smaller type is chiefly ex- 
planator}^ of the former. It is highly desirable, however, that the 
"book should be read as a whole, while the actual class-work may be 
confined to the subjects treated in the larger type, if the class is 
pressed for time. A celestial globe, and a set of star-maps (Proc- 
tor's " New Star-x\.tlas" is as good as any), will be found to be of 
use in connection with the study; and if the class has access to a small 
telescope, even, much can be learned in this way. A mere opera- 
glass will suffice to give a correct notion of the general features of 
the moon's surface, and a very small telescope, if properly used, will 
do the same for the larger planets. 



' 



CONTENTS. 

PART I. 

INTRODUCTION. 

PAGE 

Astronomy Defined — How to Study Astronomy — Angles: their 
Measure — Plane Triangles — The Sphere — Power of the Eye 
to See Small Objects — Latitude and Longitude — Symbols 
and Abbreviations 1 

CHAPTER I. 

Relation op the Earth to the Heavens. 

The Earth's Shape and Dimensions — The Celestial Sphere — The 
Horizon — The Diurnal Motion — Diurnal Motion in Different 
Latitudes — Correspondence of the Terrestrial and Celestial 
Spheres 13 

CHAPTER 11. 

Relation op the Earth to the Hkayeixs— (Continued). 

The Celestial Sphere — Systems of Coordinates — Relation of Time 
to the Sphere — Sidereal Time — Solar Time — Determinations 
of Terrestrial Longitudes — Where does the Day Change ? 
— Determination of Latitudes— Parallax 37 

CHAPTER III. 

Astronomical Instruments. 

The Telescope — Chronometers and Clocks — The Transit Instru- 
ment — The Meridian Circle — The Equatorial — The Sextant 
•—The Nautical Almanac 60 



vi CONTENTS. 

CHAPTER IV. 
Motions of the Earth. 

PAGE 

Ancient Ideas of the Phmets— Annual Revolution of the Earth 
— The Sun's Apparent Path — Obliquity of the Ecliptic — 
The Seasons — Celestial Latitude and Longitude 81 

CHAPTER V. 

The Planetary Motions. 

Apparent and Real Motions of the Planets — The Copernican 
System of the World — Kepler's Laws of Planetary Motion . . 96 

CHAPTER VI. 

Universal Gravitation. 

Newton's Laws of Motion — Gravitation in the Heavens — Mutual 
Action of the Planets— Remarks on the Theory of Gravi- 
tation 113 

CHAPTER VII. 

The Motions and Attraction op the Moon. 

Tlie Moon's Motions and Phases— The Tides— Effect of the 

Tides upon the Earth's Rotation 133 

CHAPTKR VIII. 

Eclipses of the Sun and Moon. 

The Earth's Shadow — Eclipses of the Moon— Eclipses of the 
Sun — The Recurrence of Eclipses 129 

CHAPTER IX. 

The Earth. 

Mass and Density of the Earth — Laws of Terrestrial Gravitation — 
Figure and Magnitude of the Earth — Geodetic Surveys — 
Motions of the Earth's Axis, or Precession of the Equinoxes 
—Sidereal and Equinoctial Year—The Causes of Precession 143 



CONTENTS. vii 

CHAPTER X. 

Celestial, Measurements of Mass and Distance. 

PAGE 

The Celestial Scale of Measurement — Measures of the Solar and 
Lunar Parallax — i\[ethods of Determining the Solar Parallax 
— Relative Masses of the Sun and Planets 158 

CHAPTER XI. 

The Refraction and Aberratiojt of Light ; Twilight. 

Atmospheric Refraction — Quantity and Effects of Refraction — 
Twilight — Aberration and the Motion of Light — Discovery 
and Effects of Aberration 169 

CHAPTER Xn. 
Chronology. 

Astronomical Measures of Time — Formation of Calendars — 
Kinds of IMonths and Years, Old and New Style — Divi- 
sions of the Day — Equation of Time 180 



PAET II. 

THE SOLAR SYSTEM IN DETAIL, 

CHAPTER I. 

Structure of the Solar System. 

Planets— Asteroids — Comets — Planetary Aspects — Tables of the 
Elements of the Solar System 190 

CHAPTER II. 

The Sun. 
General Summary — The Photosphere — Light and Heat from 
the Photosphere — Amount of Heat Emitted by the Sun — 
Solar Temperature — Sun-Spots and Faculae — Solar Axis 
and Equator — Nature of Sun-Spots — Number and Periodic- 
ity of Solar Spots — The Sun's Chromosphere and Corona 
—Gaseous Nature of the Prominences — The Coronal Spec- 
trum — Sources of the Sun's Heat — Theories of the Sun's 
Constitution 200 



Viii CONTENTS. 

CHAPTER III 
The Inferior Planets. 

FAGS 

Motions and Aspects — Atmosphere and Rotation of Mercury — 
Atmosphere and Rotation of Venus — Transits of Mercury 
and Venus— Supposed Intramercurial Planets 321 

CHAPTER IV. 

The Moon. 

Character of the Moon's Surface — Lunar Atmosphere — Light 
and Heat of the Moon — Is there any Change on the Surface 
of the Moon? 228 

CHAPTER V. 

The Planet Mars. 

Description of the Planet — Rotation — Surface — Satellites of 
Mars 233 

CHAPTER VI. 

The Minor Planets 

The Number of Small Planets— Their Magnitudes— Forms of 
their Orbits— Origin 237 

CHAPTER VII. 

Jupiter and his Satellites. 

The Planet Jupiter— Satellites of Jupiter 240 

CHAPTER VIIL 

Saturn and his System. 

General Description — The Rings of Saturn — Satellites of Saturn 246 

CHAPTER IX. 

The Planet Uranus. 

Discovery— Satellites 253 



CONTENTS. ix 

CHAPTER X. 
The Planet Neptune. 

PAGE 

Reasons for believing in its Existence — Discovery — Its Satellite. . 256 

CHAPTER XI. 

The Physical Constitution of the Planets. 

Mercury and Venus — The Earth and Mars — Jupiter and Saturn 

— Utanus and Neptune 261 

CHAPTER XII. 
Meteors. 

Phenomena and Causes of Meteors — Meteoric Showers — Relation 
of Meteors and Comets — The Zodiacal Light 265 

CHAPTER XIII. 

Comets, 

Aspect of Comets— The Vaporous Envelopes— Physical Consti- 
tution — Motions — Remarkable Comets — Encke's Comet — 
The Resisting Medium 274 



PAET III. 

INTRODUCTION 285 

CHAPTER I. 

Constellations. 

General Aspect of the Heavens — The Galaxy— Lucid Stars — 
Telescopic Stars — Magnitudes of the Stars— Tlie Constella- 
tions and Names of the Stars — Nunabering and Cataloguing 
the Stars . . . , , ...,,... 288 

CHAPTER IL 

Variable and Temporary Stars. 

gtars Pegularly Variable — Temporary or New Stars. .,.,.,,,.. 296 



X CONTENTS. 

CHAPTER III. 

Multiple Stars. 

PAGE 

Character of Double and Multiple Stars— Binary Systems 301 

CHAPTER IV. 

Nebula and Clusters. 

Discovery of Nebulse — Classification of Nebulae — Clusters— Star 
Clusters— Spectra of Nebulae, Clusters, and Fixed Stars- 
Motion of Stars in the Line of Sight 304 

CHAPTER V. 

Motions and Distances of the Stars. 

Proper Motions — Proper Motion of the Sun — Distances of the 
Fixed Stars 313 

CHAPTER VI. 

Construction of the Heavens. 

Star-gauging— The Milky Way 318 

CHAPTER VII. 

Cosmogony. 

Laplace's Nebular Hypothesis— General Conclush)ns 323 

INDE^ ,... 333 



ASTRONOMY 



INTEODUCTIOK 

Astronomy Defined. — Astronomy {aarrfp — a star, and 
vofAo^ — a law) is the science which has to do with the 
heavenly bodies, their appearances, their nature, and the 
laws governing their real and their apparent motions. 

In approaching the study of this the oldest of the 
sciences depending upon observation, it must be borne in 
mind that its progress is most intimately connected with 
that of the race, it having always been the basis of geog- 
raphy and navigation, and the soul of chronology. Some 
of the chief advances and discoveries in abstract mathe- 
matics have been made in its service, and the methods 
both of observation and analysis once peculiar to its prac- 
tice now furnish the firm bases upon which rest that great 
group of exact sciences which we call Physics. 

It is more important to the student that he should be- 
come penetrated with the spirit of the methods of astron- 
omy than that he should recollect its minutiae ; and it is 
most important that the knowledge which he may gain 
from this or other books should be referred by him to its 
true sources. For example, it will often be necessary to 
speak of certain planes or circles, the ecliptic, the equa- 
tor, the meridian, etc., and of the relation of the appa* 



2 ASTRONOMY. 

rent positions of stars and planets to them; but liis labor 
will be useless if it has not succeeded in giving him a pre- 
cise notion of these circles and planes as they exist in the 
sky, and not merely in the figures of his text-book. Above 
all, the study of this science, in which not a single step 
could have been taken without careful and painstaking 
observation of the heavens, should lead its student himself 
to attentively regard the phenomena daily and hourly pre- 
sented to him by Saq heavens. 

Does the sun set daily in the same point of the horizon? 
Does a change of his own station affect this and other 
aspects of the sky? At what time does the full moon rise? 
Which way are the horns of the young moon pointed? 
These and a thousand other questions are already answered 
by the observant eyes of the ancients, who discovered not 
only the existence, but the motions, of the various planets, 
and gave special names to no less than fourscore stars. 
The modern pupil is more richly equipped for observation 
than the ancient philosopher. If one could have put 2k 
mere opera-glass in the hands of Hipparchus the world 
need not have waited two thousand years to know the 
nature of that early mystery, the Milky Way, nor would it 
have required a Galileo to discover the phases of Venua 
and the spots on the sun. 

Astronomy furnishes the principles and the methods by 
means of which thousands of ships ax^e navigated with 
safety and certainty from port to port ; by which the 
dimensions of the earth itself arc fixed with high precision; 
by which the distances of the sun, the planets, and the 
brighter stars are measured and determined. The details 
of these methods cannot be given in an elementary work ; 
but the general principles and even the spirit of the special 



INTRODUCTION. 3 

methods can be entirely mastered by the faithful student. 
All the attention which he can bring will be richly reward- 
ed by the insight he will gain into the noblest of the physi- 
cal sciences. 

How to Study Astronomy. — There are a few principles 
of Mathematics, of Geography, of Physics, which must be 
clearly understood by the student commencing astronomy, 
so that he may go on with advantage, '^hey are all quite 
simple, but they must be entirely fixed in the mind, in 
order that the attention may be directed to tlie astronomical 
principle and not diverted by an attempt to recollect a fact 
from another science. Any patience and concentration 
which the student may bestow upon them at the outset 
should be rewax'dcd by the facility with which they will 
enable him to grasp tlie more interesting portions of the 
subject. The few definitions which are given in italics 
should be memorized in the words of the text. In all other 
cases it is preferable that the student should give his own 
explanations in his own words. 

First we will go briefly over some of the essential mathe- 
matical principles alluded to. 

Angles : their Measurement. — An angle is the amount 
of divergence of two right lines. For example, the angle 
between the two right lines 8'E and 
8^E is the amount of divergence of 
these lines. The angle 8^ES* is the 
amount of divergence of the two lines 
S^'E and S^E. The eye sees at once 
that the angle 8^ES* in the figure is 
greater than the angle 8^E8'^, and 
that the angle 8^E8'' is greater than fig. i. 

either of them. 




4 ASTRONOMY. 

In order to compare them and to obtain their numerical 
ratio, we must have a unit-angle. 

The unit angle is obtained in this way: The circumfer- 
ence of any circle is divided into 360 equal parts. The 
points of division are joined with the centre. The angles 
between any two adjacent radii are called degrees. In the 
figure, >S"^>S'' is about 12°, .S'^^^' is about 22°, 8'E8' is 
about 30°, and S'MS* is about 64°. The vertex of the 
angle is at the centre U: the 7neastcre of the angle is on 
the circumference S'S'^S^S\ or on any other circumference 
drawn from ^ as a centre. 

In this way we have come to speak of the length of one 
three-hundred-and-sixtieth part of any circumference as a 
degree, because radii drawn from the ends of this part 
make an angle of 1°. 

For convenience in expressing the ratios of different 
angles we have subdivided the degree into minutes and 
seconds. The degree is too large a unit for some of the 
purposes of astronomy, just as the metre is too large a unit 
for use in the machine-shop, where fine work is concerned. 

One circumference = 360° = 21600' = 1296000" 
1° = 60' = 360" 
1' = 60" 

When we wish to express smaller angles than seconds, 
we use decimals of a second. Thus one-quarter of a second 
is 0".25; one quarter of a minute is 15". 

The Radius of the Circle in Angular Measure. — If E is 
the radius of a circle, we know from geometry that 1 cir- 
cumference = 2 Tt E, where 7t = 3.1416. That is, 

'^'" "" 2 7t E = 360° = 21600' = 1296000" 

Of M = 57°,3 = 3437'.? = 206264".8. 



INTRODUCTIOK 5 

By this we mean that if a flexible cord equal in length 
to the radius of any circle were laid round the circumfer- 
ence of that circle, and if two radii were tlien drawn to the 
ends of this cord, the angle of these radii would be 57°. 3, 
3437'.7, or 206264". 8. 

It is important that this should be perfectly clear to the 
student. 

For instance, how far off must you place a foot-rule in 
order that it may subtend an angle of 1° at your eye? 
Why, 57.3 feet away. How far must it be in order to sub- 
tend an angle of a minute ? 3437.7 feet. How far for a 
second ? 206264.8 feet, or over 39 miles. 

Again, if an object subtends an angle of 1° at the eye, 

we know that its diameter must be — — as great as its dis- 

7 . o 

tance from us. If it subtends an angle of 1", its distance 

from us is over 200,000 times as great as its diameter. 

The instruments employed in astronomy may be used to 
measure the angles subtended at the eye by the diameters of 
the heavenly bodies. In other ways we determine their dis- 
tance from us in miles. A combination of these data will 
give us the actual dimensions of these bodies in miles. 
For example, the sun is about 93,000,000 miles from the 
earth. The angle subtended by the sun's diameter at this 
distance is 1922'^ What is the diameter of the sun in miles ? 

An idea of angular dimensions in the sky may be had by 
remembering that the angular diameters of the moon and 
of the sun are about 30'. It is 180° from the west point to 
the east point counting through the point immediately 
overhead. How many moons placed edge to edge would it 
take to reach from horizon to horizon ? The student may 
guess at the answer first and then compute it. 



6 



ASTRONOMY. 



Perhaps a more convenient measure is the apparent dis- 
tance apart of the '^ pointers" in the Great Dipper, which 
is 5°. (See Fig. 7, page 21.) 

Plane Triangles. — The angles of which we have been 
speaking are angles in a plane. In any plane triangle there 
are three sides and three angles — six parts. If any three of 
these parts (except the three angles) are given we can 
construct the triangle. If the three angles alone are given 
we can make a triangle which shall be of the right shape, 
and that is all. 



mm 



Fig. 2. 



Spherical Triangles. — Besides plane angles and triangles, 
we have to do with those drawn on the surface of a sphere 
— spherical triangles. This is necessary since the heavenly 
bodies are spherical in shape, and since they are seen pro- 
jected against the 'concave surface of the sky. 

The Sphere: its Planes and Circles. — In the figure, is 
the centre of the sphere and ABE is one of its circles. 
Suppose a plane AB passing through the centre and cut- 



INTnODnCTIOK 7 

ting the sphere into two hemispheres. It will intersect the 
surface of the sphere in a circle ^^^i^ which is called a 
great circle of the sphere. A great circle of the sphere is 
one cut from the surface hy a plane passing through the 
centre of the sphere. Suppose a right line POP' perpen- 
dicular to this plane. The points P and P' in which it 
intersects the surface of the sphere are everywhere 90° 
from the circle AEBF. They are the ])oles of that circle. 
The poles of the great circle CEDF are Q and Q\ 

The following relations exist between the angles made 
in the figure: 

I. The angle POQ between the poles is equal to the in- 
clination of the planes to each other. 

II. The arc BD which measures the greatest distance 
between the two circles is equal to the arc PQ which 
measures the angle POQ. 

III. The points E and F, in which the two great cir- 
cles intersect each other, are the poles of the great circle 
PQACP'Q'BD which passes through the poles of the first 
circle. 

The Spherical Triangle. — In the last figure there are 
several spherical triangles, as EDB, FAC, ECP'Q'B, etc. 
In astronomy we need consider only those Avhose sides 
are formed by arcs of great circles. The angles of the 
triangle are angles between two arcs of great circles; or what 
is the same thing, they are angles between the two planes 
which cut the two arcs from the surface of the sphere. 

In spherical triangles, as in plane, there are six parts, 
three angles and three sides. Having any three parts the 
other three can be constructed. 

The sides as well as the angles of spherical triangles are 
expressed in degrees, minutes, and seconds. If the student 



8 ASTRONOMY. 

has a globe before him, let him mark on it the triangle 
whose angles are 

^ 128° 44' 45". 1, 
B 33° 11' 12".0, 
G 18° 15' 31'M, 
and whose sides are [a is opposite to A, h to B, c to C.) 
a = 10°, i = r, c = 4°. 

Power of the Eye to see Small Objects. — When a round 
object subtends an angle of 1' (that is, wlien it is about 
3437 of its own diameters away), it is just at the limit of 
visibility, under ordinary circumstances. At the Transit of 
Venus in 1874, the planet Venus was between the earth 
and the sun, and appeared as a small black spot, just visi- 
ble to the naked eye, projected on the sun's face. It was 
^T in diameter. 

If two such discs are nearer together than 1' 12", few 
eyes can distinguish them as two distinct objects. If a 
body is long and narrow, its angular dimensions (width) 
may be reduced to 10" or 15" before it is indistinguishable 
to the eye. For example, a spider line hanging in the air. 

If an object is very much brighter than the background 
on which it is seen, there is no limit below which it is nec- 
essarily invisible. Its visibility depends, in such a case, 
only on its brightness. It is probable that the diameters 
of the brightest stars subtend an angle no greater than 
O'.Ol. 

Latitude and Longitude of a Place on the Earth's Surface. 
Geography teaches us that the earth is a sphere. Positions 
on its surface are defined by giving their latitude and 
longitude. According to geography, the latitude of a place 
on the eart¥s surface is its angular distance north or south 
of the equator. 



INTRODUCTION. 9 

The longitude of a place on the eartWs surface is its 
angular distance east or west of a given first meridia^i. 

If P ill the figure is the north pole of the earth, the 
latitude of the point B is 60° north; of Z it is 30° north; 
of / it is 27°i south. AH places having the same latitude 
are situated on the same parallel of latitude. In the figure 
the parallels of latitude are represented by straight lines. 

All places having the, same longitude are situated on the 




Fig. 3. 

same meridian. We shall give the astronomical definitions 
of these terms further on. 

It is found convenient in astronomy to modify the geo- 
graphical definition of longitude. In geography we say 
that Washington is 77° west of Greenwich, and that Syd- 
ney (Australia) is 151° east of Greenwich. For astro- 
nomical purposes it is found more convenient to count the 



10 ASTRONOMY. 

longitude of a place from the first meridian (usually 
Greenwich) always towards the west. Thus Sydney is 209° 
west of Greenwich. 360°-151"=209°. 

The earth turns on its axis once in 24 hours. In this 
time a point on its surface moves through 360 degrees, or 
such a point moves a^ the rate of 15° per hour. 360 divided 
by 24 is 15. 

Hence we may express the longitude of a place either in 
time or arc. Washington is 5^' 8™ west of Greenwich, and 
Sydney is 13^ 56™ west of Greenwich. 

It is also indifferent which first meridian we choose. 
We may refer all longitudes to Paris, to Berlin, or to Wash- 
ington. Sydney is 8^ 48™ west of Washington, and Green- 
wich is 18^ 52™ west of Washington. 

In the figure, suppose F to be west of the first meridian. 
All the places on the straight line PQ have a longitude of 
15° or 1 hour ; all on the curve P5^ Q have a longitude 
of 75° or 5 hours; and so on. 

Tlie difference of longitude of any tioo places on the earth 
is the angular distance hetioeen the terrestrial meridians 
passing through the tioo places. 

Thus Washington is 77° west of Greenwich, and Sydney 
is 209° west of Greenwich. Hence Sydney is 132° west of 
Washington, and this is the difference of longitude of the 
two places. 



SYMBOLS AND ABBREVIATIONS 





? 
© or 5 



SIGNS OF THE PLANETS, ETC. 



The Sun. 
The Moon. 
Mercury. 
Venus. 
The Earth. 



Mars. 

Jupiter. 

Saturn. 

Uranus. 

Neptune. 



The asteroids are distinguished by a circle enclosing a number, 
which number mdicates the order of discovery, or by their names, 
or by both, as (100) ; Hecate, 



Spring 
signs. 

Summer ) 
signs. ) 



SIGNS OF THE ZODIAC 

1. T Aries. 



2. » Taurus. 

3. rr Gemini. 

4. © Cancer. 

5. ^ Leo. 

6. M Virgo. 



Autumn 

signs. 



7. ^ Libra. 

8. TTi Scorpius. 

9. f Sagittarius. 

•XTTT. . C 10. \3 Capricornus, 

W mter \ ^ . . 

< 11. ^ Aquarius. 

^'S"^- 1 12. K Pisces. 



The Greek alphabet is here inserted to aid those who are not already 
familiar with it in reading the parts of the text in which its letters 
occur : 



Letters. 


Names. 


Letters. 


Names. 


A a 


Alpha 


N r 


Nu 


B ft 


Beta 


l^h 


Xi 


rr 


Gamma 


o 


Omicron 


A d 


Delta 


n Tcn 


Pi 


E B 


Epsilon 


p p 


Rho 


z c 


Zeta 


2 6 ? 


Sigma 


Hv 


Eta 


T T 


Tau 


5 


Theta 


r V 


Upsilon 


/« 


Iota 


$ <p 


Phi 


K H 


Kappa 


Xx 


Chi 


A X 


Lambda 


W rp 


Psi 


Mm 


Mu 


n 03 


Omega 



12 ASTRONOMY, 



THE METRIC SYSTEM. 

The metric system of weights and measures being employed in 
this volume, the following relations between the units of this system 
most used and those of our ordinary one will be found convenient for 
reference : 

MEASURES OF LENGTH. 

1 kilometre = 1000 metres = 0.63137 mile. 
1 metre = the unit = ,39-370 inches. 

1 millimetre = yttW of a metre = 0-03937 inch. 

MEASURES OF W^EIGHT. 

1 kilogramme = 1000 grammes = 2-2046 pounds- 
1 gramme = the unit = 15-432 grains. 



The following rough approximations may be memorized : 

The kilometre is a little more than -^^ of a mile, but less than | of 
a mile. 
The mile is 1^^ kilometres. 
The kilogramme is 2^ pounds. 

The pound is less than half a kilogramme. ^ 

One metre is 3-3 feet. -^ 

One metre is 39*4 inches. 



CHAPTER I. 
THE RELATION OF THE EARTH TO THE HEAVENS. 

The Eauth's Shape and Dimensions. 

The earth is a globe whose dimensions are gigantic 
when compared with our ordinary and daily ideas of size. 

Its shape is nearly a sphere, as has been abundantly 
proved by the accurate geodetic surveys which have been 
made by various nations. 

Of its size we may get a rough idea by remembering 
that at the present time it requires about three months to 
travel completely around it. 

To these familiar facts we may add two propositions 
which are fundamental in astronomy. 

I. Tlie earth is completely isolated in space. The most 
obvious proof of this is that men have visited nearly every 
part of the earth's surface without finding anything to the 
contrary. 

II. TJie earth is one of a vast number of globular bodies, 
familiarly hnoioi as stars and planets, moving according 
to certain laius and separated by distances so immense that 
the magnitudes of the bodies themselves are insignificant in 
comparison to these distances. The first conception which 
the student of astronomy has to form is that of living on 
the surface of a splierical earth which, although it seems of 
immense size to him, is really but a point in comparison 



14 A&TRONOMT. 

with the distances which separate him from the stars which 
he nightly sees in the sky. 

The Celestial Sphere. 

When we look at a star at night we seem to see it set 
against the dark surface of a hollow sphere in whose centre 
we are. 

All the stars seem to be at the same distance from us. 
When we stop to consider, we see that it is quite possible 
that some one of the many stars visible may be nearer 
than some other, but as we have no immediate method 
of knowing which of two stars is the nearer, we are driven 
to speak of their apparent positions just as if they were 
bright points studded over the inner surface of a large 
hollow globe, and all at the same distance from us. The 
radius of this globe is unknown. We do not, however, 
think of any of the stars as beyond the surface and 
shining through it. We therefore suppose the radius of 
the sphere to be equal to or greater than the distance of 
the remotest star. 

Students generally fail at the outset to realize two very 
important facts in relation to the celestial sphere. First, 
that for all the purposes of our present knowledge the 
relative positions of the stars on its surface do not vary. 
Maps were made of these positions centuries ago which are 
as correct now as old maj^s of portions of the earth. The 
motions of the earth present different portions of the celes- 
tial sphere to our observation at different times, and one 
who has not thought at all of the subject might by that 
fact be led to suppose that changes are taking place in the 
relative positions of the stars themselves. Most people, 
however, know that they can find the same groups of stars 



RELATION OF THE EARTH TO THE HEAVENS. 15 

— '' constellations," as they are called — in different direc- 
tions from the observer's location on the earth, night after 
night; the difference in the directions being due to the 
earth's motions. Eeflection on the foregoing will help the 
student to realize the second important fact alluded to in the 
beginning of this paragraph — that for most practical pur- 
poses of astronomy the earth may be regarded as a point 




Fig. 4. 



in the centre of a hollow globe whose inside surface is 
spotted oyer with the stars, that hollow globe corresponding 
to the celestial sphere. In fact ingenious instruments to 
ilUistrate some of the truths of astronomy have been made 
of large globes of glass or other transparent substances, 
with the stars painted in their unvarying positions on the 



16 ASTRONOMY, 

inside surface, and the earth suspended at the centre by 
supports rendered as nearly invisible as possible. 

Suppose an observer at the point in the figure. If he 
sees a star at the point § it is clear that the real star may 
be anywhere in space on the line OQ, as at q for example, 
and still appear to be at Q. 

Again, stars which appear to be at the points P, F, U, 
T, S, R, may in fact be anywhere on the lines P, F, 
U, T, S, R. Thus, if there were three stars along 
the line T, they would all be ])rojected at the point T of 
the celestial sphere, and would appear as one star. 

The celestial sphere is the surface upon lohich we im- 
agine the stars to he projected. 

Tha projection of a body upon the celestial sphere is tlie 
point in which this body appears to be, when seen from 
the earth. This point is also called the apparent position 
of the body. Thus to an observer at 0, T is the apparent 
position of any of the stars whose true positions are t, t, t. 
Hence it follows "that positions on the celesticd sphere re- 
present the directions of the heavenly hodies from the ob- 
server, hut have no necessary relation to their distances. 

If the observer changes his position, the apparent posi- 
tions of the stars will also change. 

We need some method of describing the apparent posi- 
tions of stars on the celestial sphere; to do this we im- 
.•igine a number of great circles to be drawn on its surface, 
and to these circles we refer the apparent positions of the 
stars. 

A consideration of Fig. 2 will show ilie correctness of 
the following propositions, which it is necessary should be 
clearly understood : 

I. Every straight line through the observer, when pro- 



RELATION OF THE EARTH TO THE HEAVENS. 17 

duced indefinitely, intersects the celestial sphere in two 
opposite j)oints. 

II. Every plane througli the observer intersects the 
sphere in a great circle. 

III. For every such plane there is one line through the 
observer's position which intersects the plane at light 
angles. This line meets the sphere at the poles of the 
great circle which is cut from the sphere by the plane. 

Example: P P' , Fig. 2, is a line through perpendicular 
to the plane A B. P, P' are the poles of A B. ' 

IV. Every line through the centre has one plane perpen- 
dicular to it, which plane cuts the sphere in a great circle 
whose poles are the intersection of the line with the 
sphere. 

Example: The line QQ' has one plane CD through 
perpendicular to it, and only this one. 

The Horkon. 

A level 2^lcine touching the spherical earth at the point 
where an observer stands is called the horizon of that 
ohserver. 

This plane cuts the celestial sphere in a great circle, 
which is called the celestial horizon. The celestial horizon 
is therefore the boundary between the visible and the in- 
visible hemispheres to that observer. 

The Vertical Line.— The vertical line of any observer is 
the direction of a plumb-line where he stands. This line 
is perpendicular to his horizon. It intersects the celestial 
sphere in two points, called the zenith and the nadir of 
that observer. 

The zenith of aii observer is the point lohere his vertical 
line cuts the celestial sphere above his head. 



18 



ASTRONOMY. 



The 7iadir of an observer is the point where his vertical 
line cuts the celestial sphere lelow his feet. 

The zenith and nadir are the poles of the horizon. 
Vertical Planes and Circles. — A vertical plane with re- 
spect to any observer is a plane which contains his vertical 
line. It must pass through his zenith and nadir and must 
be perpendicular to his horizon. 

A vertical plane cuts the celestial sphere in a vertical 
circle. 
As soon as we imagine an observer to be at any point on 

the earth's surface his horizon 
is at once fixed; his zenith 
and nadir are also fixed. From 
his zenith radiate a number 
of vertical circles which cut the 
celestial horizon perpendicu- 
larly, and unite again at his 
nadir. This is a system of 
lines and circles which every 
YiG.h. person carries about with 

him, as it were, and which may serve him for lines to 
which to refer the apparent position of every star which he 
sees. 

Some one of these vertical circles will pass through any 
and every star visible to this observer. 

The altitude of a heave7ily body is its elevation above the 
plane of the horizon measured on a vefiical circle through 
the star. 

The zenith distance of a star is its angular distance from 
the zenith measured on a vertical circle. 

In the figure, Z 8 is, the zenith distance (<^) of S, and 
H8 (a) is its altitude. Z S E is m arc of a great circle; 




BELATION OF THE EARTH TO THE HEAVENS. 19 

the vertical circle through the star. ZS H = a-\- ^= 90°, 
and ^ = 90° - aora = 90° - «?. 

The altitude of a star in the zenith is 90°; half way from 
the zenith to the horizon it is 45°; in the horizon it is 0°. 

The azimuth of a star is the angular distance from the point 
ivhere the vertical circle through it meets the horizon, to the 
north {or south) poijit of the hoinzon. 

In the figure, NH is the azimuth of S. The azimuth 
of a star in the east or west is 90°. 

The prime vertical of an observer is that one of his verti- 
cal circles which passes through his east and west points. 

Co-ordinates of a Star. — The apparent position of a heav- 
enly body is completely fixed by means of its altitude and 
azimuth. If we know the altitude and azimuth of a star 
we can point to it. 

If, for example, its azimuth is 20° from north towards 
the west and if its altitude is 30°, we can point to the star by 
measuring an angle of 20° from the north point towards 
the west, which will fix the foot of a vertical circle through 
the star. The star itself will be on the vertical circle, 30° 
above the horizon. 

This point, and this alone, will correspond to the posi- 
tion of the star as determined by its altitude and azimuth. 

Numbers {or quantities) which exactly define the position 
of a body are called its co-ordinates. 

Hence altitude and azimuth form a pair of co-ordinates 
which fix the apparent position of a star on the celestial 
sphere. 

It must be remembered that these two co-ordinates give 
only the position of the projection of the star on the celes- 
tial sphere, and give no knowledge of its distance from the 
observer, The body may be any where on the line define^ 



20 ASTRONOMY. 

by the position on the celestial sphere and the place of the 
observer. 

If we also know the distance of the star from the obser- 
ver, we know every possible fact as to its place in space. 

Thus, three co-ordinates suffice to fix the absolute position 
of a body in space ; two co-ordinates suffice to determine its 
apparent position on the celestial sphere. 

These propositions suppose the place of the observer to 
be fixed, since the altitude and azimuth refer to an obser- 
ver in some one definite position. If the observer should 
change his place, the star remaining fixed, the apparent 
position of the star on the celestial sphere would change to 
him, owing to his own motion. The numbers which ex- 
press this apparent position — the altitude and azimuth of 
the star — would also change. 

But wherever the observer is, if he has these two co- 
ordinates for a star, the apparent place of the star is fixed 
for Mm. 

The Horizon. — Since the earth is spherical in form, and 
the horizon is a plane touching this sphere, every different 
place must have a different horizon. Wherever an observer 
goes on the earth's surface he carries an horizon, a zenith, 
and a nadir with him, and a set of vertical circles to which 
he can refer the positions of all the stars he sees. If he 
stays at a fixed point on the earth's surface his horizon is 
always fixed with relation to his vertical line. But the 
earth on which he stands is turning round its axis, and his 
horizon being tangent to the earth is moving also, and the 
vertical line moves with it. The stars stay in the same abso- 
lute places from year to year. The earth on which the 
observer stands is turning round from west to east. His 
horizon is thus brought successively to the east of the various 



RELATION OF TEE EARTH TO THE HEAVEN8. 21 

stars, which thus appear to rise higher and higher above 
it. 

The earth continues its motion, and the plane of his ho- 
rizon finally approaches the same stars from the west and 
they set below it, only to repeat this phenomenon with 
every rotation of the earth. 

The horizon appears to each observer to be the stable 
thing, and the motion is referred to the stars. As a matter 
of fact it is the stars that stand still and the horizon which 
moves below them, causing them to appear to rise, and then 
above them, causing them to appear to set. 

The Diuknal Motion. 

The diurnal inotion is that apparent motion of the sun, 
moon, and stars from east to ivest in C07isequence of luhich 
they rise and set. 

We call it the diurnal motion because it repeats itself 
from day to day. The diurnal motion is caused by a daily 
rotation of the earth on an axis passing through its centre 
called the axis of the earth. 

This axis intersects the earth's surface in two opposite 
points called the north and south poles of the eartli. If the 
earth's axis be prolonged in both directions, it meets the 
celestial sphere in two points which are called the poles of 
the celestial sphere or the celestial poles. The north celes- 
tial pole corresponds to the north end of the earth's axis; 
the south celestial pole to the south end. 

The plane of the equator is that plane which passes 
through the earth's centre perpendicular to its axis. This 
plane intersects the earth's surface in a great circle of the 
earth's sphere which is called the earth's equator {e q in 
I^ig. 6). 



22 A8TE0N0MT. 

This plane intersects the celestial sphere in a great circle 
of this sphere which is called the celestial equator or equi- 
noctial {EQ in Fig. 6). 

The celestial equator is everywhere half way between the 
two celestial poles and thus 90° from each. The celestial 
poles are thus the poles of the celestial equator. 

Apparent Diurnal Motion of the Celestial Sphere. — The 




Fia. 6. 



observer on the earth is unconscious of its rotation, an(^ 
the celestial sphere appears to him. to revolve from east to 
west around the earth, while the earth appears to remain 
at rest. The case is much the same as if he was on a 
steamer which is turning round, and as if he saw the har- 
bor-shores, the ships, and the houses apparently turning in 
an opposite direction, 



RELATION OF THE EARTE TO THE HEAVENS. 23 

So far as appearances are concerned, it is quite the same 
thing whether we conceive the earth to be at rest and the 
heavens to turn about it, or whether we conceive the stars 
to remain at rest and the earth to move on its axis. We 
can explain all the phenomena of the diurnal motion in 
either way. We must, however, remember that it really is 
the earth which turns on its axis and successively presents 
to the observer different parts of the celestial sphere. The 
parts to his east are just coming into view (rising above his 
horizon). The parts to his west are about to disappear, 
(setting below his horizon). 

Since the diurnal motion is an apparent rotation of the 
celestial sphere about a fixed axis, -it follows that there 
must be two points of this sphere that remain at rest; 
namely, the two celestial poles. Moreover, since the celes- 
tial poles are opposite points, one pole must be above the 
horizon and therefore a visible point of this sphere, and 
the other pole must be below the horizon and therefore in- 
visible. 

The celestial pole visible to observers in the northern 
hemisphere is the north pole. To locate its place in the 
sky let the student look at the northern sky on any clear 
evening. 

He will see the stars somewhat as they are represented in 
the figure. 

In fact Fig. 7. shows the stars as they will appear to 
an observer in the month of August in the early hours of 
the evening. But the configurations of the stars can be 
recognized at any other time. 

The first star to be identified is Polaris, or the Pole Star. 
It may be found by means of the Pointers, two stars in the 
constellation Ursa Major, familiarly known as the Great 



S4 



ASTRONOMY. 



Dipper. The straight line through these stars, as shown 
in the figure, passes near Polaris. Polaris is li degrees 
from the true pole. There is no star exactly at the pole 
itself. 

The altitude of the pole-star above the horizon of any 
place is equal to the latitude of the place, as will be shown 




Fig. 7. 



hereafter. Hence in most parts of the United States the 
north pole is from 30° to 45° above the horizon. In Eng- 
land it is 51°, in Norway 60°. 

TJie 7iortli-polar distance of a star is its angular distance 
from the north celestial pole. 



ttELATtOl^ OF THE EARTH TO THE HEAVENS. 25 

The following laws of the diurnal motion will now be 
clear: 

I. Every star in the heavens appears to describe a circle 
utound the pole as a centre in consequence of the diurnal 
motion. 

IL Tlie greater iM starts north-polar distance the larger 
is the circle. 

III. All the stars describe their diurnal orbits in the 
same interval of time, which is the time required for the 
earth to turn once on its axis. 

The circle which a star appears to describe in the sky in 
consequence of the diurnal motion of the earth is called the 
diurnal orbit of that star. 

These laws can be proved by observation. The student 
can satisfy himself of their correctness in any clear night. 

If the star's north-polar distance is less than the altitude 
of the pole, the circle which the star describes will not 
meet the horizon at all, and the star will therefore neither 
rise nor set, bat will simply perform an apparent diurnal 
revolution round the pole. Such stars are shown in the 
figure. The apparent diurnal motion of the stars is in the 
direction shown by the arrows in the cut. Below the 
pole the stars appear to move from left to right, west to 
east; above the pole they appear to move from east to 
west. 

The circle within which the stars neither rise nor set is 
called the circle of perpetual apparition. The radius of 
this circle is equal to the altitude of the pole above the 
horizon, or to the north polar distance of the north point 
of the horizon. 

As a result of this apparent motion each individual con- 
stellation changes its configuration with respect to the 

r 



se 



A^momMT. 



horizon. That part of the constellation Which is highest 
when the group is above the pole becomes lowest when it 
is below the pole. This is shown in the figure, which 
represents a supposed constellation at different times of the 
night as it revolves round the pole. The cidminatmi of a 
star occurs when it is at its highest point above the hori- 
zon. The point of culmination is midway between the 
points of rising and setting. 
If the polar distance of a star exceeds the altitude of the 




pole, the star will dip below the horizon for a part of its 
diurnal orbit, and the greater the polar distance of the 
star the longer it will be below the horizon. 

A star whose polar distance is 90° lies on the celestial 
equator, and one half of its diurnal orbit is above and 
one half below the horizon. i 

The sun is in the celestial equator about March 21st and 
September 21st of each yeai, so that at th^se times the 



nMLATtON OF T^E EAttTB TO THE SEAVEN8. g7 

days and nights are of equal length. This is why the 
celestial equator was formerly called the equinoctial. 

Looking further south at the celestial sphere, we shall 
see stars which rise a little to the east of the south point of 
the horizon and set a little to the west of this point, being 
above the horizon but a short time. The south pole is as 
far below the horizon of any place as the north pole is above 
it. Hence stars near the south pole never rise in our 
latitudes. The circle within which stars never rise is called 
the circle of pei'pehial occuUation. 

It is clear that the positions of the circles of perpetual 
apparition and occultation depend upon the position of the 
observer upon the earth, and hence that they will change 
their positions as the observer changes his. 

By going to Florida we may see groups of stars which 
are not visible in the latitude of New York. 

The Meridian. — The plane of the meridiaii of an observer 
is that one of his vertical planes luhich co7itains the earths 
axis. Being a vertical plane it must contain the zenith 
and nadir of the observer ; as it contains the earth's axis 
it must contain the north and south celestial poles. 

Different observers have different meridian planes, since 
they have different zeniths. 

The terrestrial meridian of an observer is the line in 
which the plane of his meridian intersects the surface of 
the earth. It is his north and south line. 

It follows that if several observers are due north and 
south of each other, they have the same terrestrial meridian. 

The celestial meridian of an observer is the great circle 
cut from the celestial sphere by the plane of that observer's 
meridian. Persons on the same terrestrial meridian have 
the same celestial meridian. 



§8 



ASfROi^bMY. 



Terrestrial meridians are considered as belonging to tlid 
places through which they pass. For example, we speak 
of the meridian of Greenwich or of the meridian of Wash- 
ington, and by this we mean the (terrestrial or celestial) 
meridian lines cut out by the meridian plane of the Royal 
Observatory at Greenwich or the Naval Observatory at 
Washington. 

The Diurnal Motion in Different Latitudes. 

As we have seen, the celestial horizon of an observer will 
change its place on the celestial sphere as the observer travels 




Fig. 9. The Parallel Sphere. 



from place to place on the surface of the earth. If he 
moves directly toward the north his zenith will approach the 
north pole; but as the zenith is not a visible point, the 
motion will be naturally attributed to the pole, which will 
seem to approach the point overhead. The new apparent 
position of the pole will change the aspect of the observer's 
sky, as the higher the pole appears above the horizon the 



RELATION OP THE EARTH TO THE HEAVENS. ^9 

greater the circle of perpetual apparition, and therefore the 
greater the number of stars which never set. 

If the observer is at the north pole his zenith and the 
pole itself will coincide : half of the stars only Avill be vis- 
ible, and these will never rise or set, but appear to move 
around in circles parallel to the horizon. The horizon and 
the celestial equator will coincide. The meridian will be 
indeterminate since ^and P coincide; there will be no east 
and Avest line, and no direction but south. The sphere in 
this case is called ajjarallel sphere, (See Fig. 9.) 




Fig. 10.— The Eight Sphere. 

If instead of travelling to the north the observer should 
go toward the equator, the north pole would seem to ap- 
proach his horizon. When he reached the equator both 
poles would be in the horizon, one north and the other 
south. All the stars in succession would then be visible, 
and each would be an equal time above and below the 
horizon. (See Tig. 10.) 

The sphere in this case is called a right sphere, because 
the diurnal motion is at right angles to the horizon. If 



go ASmONOMT. 

now the observer travels southward from the equator, the 
south pole will become elevated above his horizon, and in 
the southern hemisphere appearances will be reproduced 
which we have already described for the northern, except 
that the direction of the motion will, in one respect, be 
different. The heavenly bodies will still rise in the east 
and set in the west, but those near the equator will pass 
north of the zenith instead of south of it, as in our lati- 
tudes. The sun, instead of moving from left to right, 
there moves from right to left. The bounding line be- 
tween the two directions of motion is the equator, where 
the sun culminates north of the zenith from March till 
September, and south of it from Sej^jtember till March. 

If the observer travels west or east of his first station, 
his zenith will still remain at the same angular distance 
from the north pole as before, and as the phenomena 
caused by the earth's diurnal motion at any place depend 
only upon the altitude of the elevated pole at that place, 
these will not be changed except as to the times of their 
occurrence. A star which appears to pass through the 
zenith of his first station will also appear to pass through 
the zenith of the second (since each star remains at a con- 
stant angular distance from the pole), but later in time, 
since it has to pass through the zenith of every place be- 
tween the two stations. The horizons of the two stations 
will intercept different portions of the celestial sphere at 
any one instant, but the earth's rotation will present the 
same portions successively, and in the same order, at both. 



RELATION OF TEE EARTH TO THE HEAVENS. 31 



Correspondence of the Terrestrial and Celestial 
Spheres. 

We have seen that the altitude of the pole above the 
horizon of any observer changes as the observer changes 
his place on the earth's surface. The exact relation of the 
altitude of the pole and the horizon of any observer is 
expressed in the following Theorem: The altitude of the 
celestial pole alove the horizon of any place on the eartNs 
surface is equal to the lati- 
tude of that place. 

Let Z be a place on the 
earth P Ep Q, Pp being 
the earth's axis and E Q its 
equator. Z is the zenith of 
the place, and ^i? its hori- 
zon. L Q is the latitude 
of L according to ordinary 
geographical definitions; i.e., 
it is the angular distance of 
L from the equator. Pro- 
long P indefinitely to P' 
and draw L P" parallel to it, 
the celestial sphere infinitely distant from L- In fact 
they appear as one point since the dimensions of the earth 
are vanishingly small compared with the radius of the 
celestial sphere, which may be taken as large as we please. 
We have then to prove that L Q = P" L H. P OQ 
and ZL IT are right angles, and therefore equal. Z L P" 
= ZOP' by construction. Hence Z L H - Z L P" =^ 
P Q — Z P'y ox the latitude of the point L is mea^^ 
ui^ed by either of the e(|ual angles L Q ox P" L.Jl. 




Fig. 11. 

P' and P" are points on 



32 ASTRONOMY. 

If we denote the latitude by q) it follows that the N.P.D. 
(north-polar distance) of Z is 90° — cp. As an observer 
moves to various parts of the earth, his zenith changes 
position with him. In every position the N.P.D. of his 
zenith is 90° — cp. If he is at the equator his q) is 0° and 
his zenith is 90° from the north pole, which must there- 
fore be in his horizon. If he is at the north pole, cp = -\- 
90° and the N.P.D. of his zenith is 0°, or his zenith co- 
incides with the north pole. If he is at the south pole 
{cp = - 90°) the N.P.D. of his zenith is 90° - (- 90°) 
or 180°. That is, his zenith is 180° from tlie north pole, 
or it must coincide with the south pole ; and so in other 
cases. 

All this has just been shown (pages 28-30) in another 
way, but it is of the first importance that it should be not 
only clear but familiar to the student. When he sees any 
astronomical diagram in which the north pole and the hori- 
zon are laid down he can at once tell for what latitude this 
diagram is constructed. The elevation of the pole above 
the horizon measures the latitude of the observer, to whose 
station this particular diagram applies. 

Change of the Position of the Zenith of an Observer by 
the Diurnal Motion. — In Fig. 12 suppose nesq to repre- 
sent the earth and N E 8 Q the celestial sphere. The earth, 
as we know, is rotating on the axis NS. We have now to 
inquire what are the real circumstances of this motion. 
The apparent phenomena have been previously described. 
Remember that the vertical line of an observer is (practi- 
cally) that of a radius of the earth passing through his 
station. If the observer is at n his zenith is at N. As 
the earth revolves the zenith will revolve also. If the ob- 
server is in 45° north latitude, he is carried |*ound bv the 



RELATION OF THE EARTH TO THE HEAVENS. 33 

lofetion of the earth in a small circle of the earth's surface 
whose plane is perpendicular to the earth's axis. This is 
the parallel of 45°, so called, and is indicated in the figure. 
His zenith is always directly above him, and therefore his 
zenith must describe each day a circle M L on the celestial 
sphere corresponding to this parallel on the earth; that is. 




Fia. 12. 

a circle half way between the celestial pole and the celestial 
equator. Now, suppose the observer to be on the equator 
e q. His zenith will then be 90° from either pole. As the 
earth revolves on its axis his zenith will describe a great 
circle B Qon the celestial sphere. This circle is the celestial 
ecjuator. An obseryer at 45° south latitude will have a 



34 ASTRONOMY. 

parallel SO marked out on the celestial sphere by the 
motion of his zenith due to the earth's rotation, and so on. 
Thus, for each parallel of latitude on the earth we have a 
corresponding circle on the celestial sphere, and each of 
these latter circles has its poles at the celestial poles. 

Not only are there circles of the celestial sphere which 
correspond to parallels of latitude on the earth, but there 
are also celestial meridians corresponding to the various 
terrestrial meridians. The plane of the meridian of any 
place contains the zenith of that place and the two celestial 
poles. It cuts from the earth's surface the terrestrial 
meridian and from the celestial sphere that great circle 
which we have defined as the celestial meridian. To fix 
the ideas let us suppose an observer at some one point of 
the earth's surface. A north and south line on the earth 
at that point is the visible representative of his terrestrial 
meridian. A plane through the centre of the earth and 
that line contains his zenith, and cuts from the celestial 
sphere the celestial meridian. As the earth rotates on its 
axis his zenith moves around the celestial sphere in a 
parallel as Z L in the last figure. Suppose that the east 
point is in front of the picture, the west point being be- 
hind it. Then as the earth rotates the zenith Z will move 
along the line Z L from ^towards L. The celestial meri- 
dian always contains the celestial poles and the point Z, 
wherever it may be. Hence the arcs of great circles join- 
ing N.P. and S.P. in the figure are representatives of the 
celestial meridian of this observer, at different times dur- 
ing the period of the earth's rotation. They have been 
drawn to represent the places of the meridian at intervals 
of 1 hour. That is, 12 of them are drawn to represent 
X% consecutive positions of the meridian during a semi^ 



RELATION OF THE EARTH TO THE HEAVENS. 35 

revolution of the earth. In this time Z moves from Z to 
L, In the next semi-revolution Z moves from L to Z, 
along the other half of the parallel Z L. In 24 hours 
the zenith Z of the observer has moved from Z to L and 
from L back to Z again. The celestial meridian has also 
swept across the heavens from the position JV^.F., Z, Q, S, 
S.P. through every intermediate position to JSf.P., L, E, 0, 
S.P., and from this last position back to N.P., Z, Q, S, 
S.P. The terrestrial meridian of the observer has been 
under it all the time. This real revolution of the celestial 
meridian is incessantly repeated with every revolution of 
the earth. The sky is studded with stars all over the 
sphere. The celestial meridian of any place approaches 
these various stars from the west, passes them, and leaves 
them. This is the real state of things. Apparently the 
observer is fixed. His terrestrial and celestial meridians 
seem to him to be fixed, not only with reference to himself, 
as they are, but to be fixed in space. The stars appear to 
him to approach his celestial meridian from the east, to 
pass it, and to move away from it towards the west. 
When a star crosses the celestial meridian it is said to 
culminate. The passage of the star across the meridian is 
called the transit of that star. This phenomenon takes 
place successively for each observer on the earth. Suppose 
two observers, A and B, A being one hour (15°) east of 
B in longitude. This means that the angular distance of 
their terrestrial meridians is 15° (see page 10). From what 
we have just learned it follows that their celestial meri- 
dians are also 15° apart. When B's meridian is iV.P., 
Z, Q, R, S.P., A's will be the first one (in the figure) 
beyond it; when B's meridian has moved to this first posi- 
tion, A's will be in the second, and so on, always 15° 



36 ASTRONOMT. 

(1 hour) in advance. A group of stars which has just come 
to A's meridian will not pass B's for 1 hour. When they 
are on B's meridian they will be 1 hour west of A's, and 
so on. Notice also that A's zenith is always 15° east of 
B's. 

The same stars will successively rise, culminate, and set 
to each observer, but the phenomena will be presented to 
the eastern observer sooner than to the other. 



CHAPTER IL 

THE RELATION OF THE EARTH TO THE HEAVENS— 
{Continued.) 

The Celestial Sphere. 

Systems of Co-ordinates.— The great circles of the celestial 
sphere which pass through the two celestial poles are called 
hour-circles. Each hour-circle is the celestial meridian of 
some place on the earth. 

The hour-circle of any particular star is that one which 
passes through the star at the time. As the earth revolves, 
different hour-circles, or celestial meridians, come to the 
star. 

In Fig. 13 let be the position of the earth in the centre of 
the celestial sphere NZ SD. Let ^be the zenith of the ob- 
server at a given instant, and P, p, the celestial poles. By 
de^nition F Z S p n N F is his celestial meridian. (Each 
of these points has a name; let the student give the names 
in order.) NS is the horizon of the observer at the instant 
chosen. FO N is his latitude. If F is the north pole, he 
is in latitude 34° north, (See page 31.) 

U C WD is the celestial equator; E and W are the east 
and west points. The earth is turning from W to E. That 
is, the celestial meridian which at the instant chosen in the 
picture contains F Zp was in the position F D Rp twelve 
bours earlier. 



38 



ASTRONOMY. 



F (7, P B, P V, P J) are parts of liour-circles. If A is 
a star, P B \s the liour-circlo of that star. As the eartli 
turns P B turns with it, and directly P B will have moved 
away from A towards the top of the picture and soon P V 
will pass through the star A, which stands still. When it 
does, PV will be the hour-circle of A. At the instant 
chosen P B is the hour-circle of A. The stars inside the 
circle NK are always above the observer's horizon, hn is 




Fia. 13. 



half of the diurnal orbit of one of the north stars. All the 
stars inside the circle SB are perpetually invisible to the 
observer, o r is half of the orbit of one of these southern 
stars. The north-polar distance of all those stars perpetu- 
ally above the horizon is less than or equal to PA^; the 
south-polar distance of all the stars perpetually invisible is 
less than or equal to p S, which is equal to P N, 



RELATION OF THE EAUTH TO THE HEAVENS. $9 

Altitude and Azimuth. — Z G is the vertical circle of the 
star A at the instant chosen for making the picture. In 
a few moments Z will have moved eastwards and a new 
vertical circle will have to be drawn. OA is the altitude 
of A at the instant; in a few moments it will be less. J^'or 
as Z moves towards the eastward, NWS, the western hori- 
zon of the observer, will move upwards (in the drawing) 
and come nearer to A, which stands still. Therefore the 
altitude of A will diminish i)rogressively. It is now GA, 

The azimuth of A is now N G, counted from the north 
point. It will change as Z changes. Having the altitude 
and azimuth of A at the instant, the observer at can find 
it in the sky. (See page 18.) 

North-Polar Distance and Hour-Angle. — The north-polar 
distance of A is PA. This will serve as one of a pair of 
co-ordinates to point out the apparent position of A in the 
sky. 

The hour-angle of a star is the angular distance letiveen 
the celestial meridian of the place and the hour-circle of 
that star. The hour-angle is counted from the meridian 
towards the west from 0" to 360°, or from 0^» to 24'\ The 
hour-angle of A, at this instant, is Z F B. The hour- 
angle of a star A" is 0°. 

The hour-angle is measured by the arc of the equator 
between the celestial meridian and the foot of the hour- 
circle through the star. The arc C B measures the hour- 
angle of A at the instant. Directly, Z will have moved away 
to the east and G will move away also along the dotted part 
of the line representing the equator, W G E D. 

Having the two co-ordinates PA and G B, the observer 
at can find the star A. It will be noticed that these two 
co-ordinates, polar distance and hour-angle, differ in one 



40 ASTRONOMt. 

respect from the two co-ordinates altitude and azimuth. 
Both the latter change as the earth revolves on its axis. Of 
the former only one changes; viz., the hour-angle. The 
polar distance of a star remains the same, since it is the dis- 
tance from a fixed point, the pole, to a fixed point, the star. 

Right Ascension and North-Polar Distance. — We can 
devise a pair of co-ordinates neither of which shall change 
as the earth revolves. This will clearly be convenient, for 
this pair of co-ordinates will be the same for every observer 
and for every hour of the day, whereas the others vary with 
the time, and with the situation of the observer. 

To select such a pair we have simply to use fixed points 
in the celestial sphere to count from. The north pole will 
do for one of these, and the north-polar distance of the star 
will serve for one co-ordinate. This is measured, for the 
star Af on the hour-circle P B, Let us choose some fixed 
point V on the equator to measure our other co-ordinate 
from, and let us always measure it on the equator towards 
the east from 0° to 360° (from O'^ to 24^). That is, from 
V through Bj C, E, i>, W, successively. 

V B is the right ascension of A. The right ascension of 
a star is the angular distance of the foot of the hour-circle 
through the star from the vernal equinox, measured on the 
celestial equator y towards the east. 

Exactly what the vernal equinox is we shall find out 
later on; for the present it is sufiicient to define it as a 
certain fixed point on the celestial equator. 

If we have the right ascension and north-polar distance 
of a star, we can point it out. Thus V B and PA define 
the position of ^. As long as the pole, the star, and the 
vernal equinox do not move relatively to each other these 
two co-ordinates fix the position of the star. Their relative 



DELATION OF THE EARTH TO THE HEAVENS. 41 

positions are not affected by the rotation of the earth, nor 
by the position of the observer upon its surface. He may 
be in any latitude or any longitude, and his zenith may be 
anywhere in the whole sky, but the right ascension and 
the north-polar distance of each star remain the same nev- 
ertheless. 

The right ascension of the star X is F (7. Of a star at E 
it is FC^; of a star at D it is YGED \ of a star at W 
it is FC^DPF, and so on. 

Right Ascension and Declination. — Sometimes in place 
of the north-polar distance of a star it is convenient to 
use its declination. 

The declination of a star is its angular distance north or 
south of the celestial equator. 

The declination of A is BA, which is 90° minus PA. 

The relation between N. P. D. and S is 

N. P. D. = 90° - ^; S= 90° - N. P. D. 

North declinations are +; South declinations are — •. 

The declination oi Z \b C Z. CZ is equal to F J^, since 
each is equal to 90° — PZ. PN measures the latitude of 
the observer whose zenith is Z. (See page 31.) 

The latitude of a place on the eartWs surface is measured 
by the declination of its zenith. 

This is the definition of the latitude which is used in 
astronomy. 

Co-ordinates of a Star. — In what has gone before we have 
seen that there are various ways of expressing the apparent 
positions of stars on the surface of the celestial sphere. 
That one most commonly used in astronomy is to give the 
right ascension and north-polar distance (or declination) of 
the star. The apparent position of the star is fixed by these 



42 asthohomt. 

two co-ordinates. If we know its distance also, the abso- 
lute position of the star in space is fixed by the three co- 
ordinates. Thus we haye a complete method of describing 
the positions of the heavenly bodies. 

Co-ordinates of an Observer. — To describe the position of 
an observer on the surface of the earth we have to give his 
latitude and longitude. His latitude is the declination of 
his zenith; his longitude is the fixed angle between his 
celestial meridian and the celestial meridian of Greenwich 
(or Washington). Declination in the sky is analogous to 
Latitude on the earth. Right ascension in the sky is anal- 
ogous to Longitude on the earth. Both of these co-ordi- 
nates depend upon the position of his zenith, since his 
longitude is nothing but the angular distance of his zenith 
west of the zenith of Greenwich. 

All this is extremely simple, but if it is clearly under- 
stood the student has it in his power to answer a great 
many interesting questions for himself. 

We know, for example, that the sun is in the equator and at the 
vernal equinox on March 21st of each year. 

The student can determine for himself what appearances will be 
presented on that day next year. He may proceed in this way: Draw 
a circle to represent the celestial sphere. Take a point, P, of it to 
be the position of the north pole in the sky. If the observer lives 
in a place whose latitude is qj degrees north, his zenith will be 
QC" — qi from the north pole measured towards the south. Measure 
off 90° — ^ on the circle from P. The end of that arc is the zenith 
of that observer, Z. PZ is an arc of his celestial meridian. Meas- 
ure from P through Z 90"*, and the end of that arc is on the equator, 
Q say. Join P with the centre, 0, of the circle. This line is the 
direction of the celestial pole. Join and Q, and this line (perpen- 
dicular to PO) is the direction of that point of the equator which is 
highest above his horizon. Draw the line ZO; this is the vertical 
line. Through draw NOS perpendicular to Z 0. This is the north 
and south line of his horizon. Draw the ovals which represent (in 



RELATION OF THE EARTH TO THE HEAVENS. 43 

perspective) the circles of the equator and of the horizon. Assume 
a point, V, of the celestial equator. On March 21st of each year the 
sun is there. When the sun is at the highest point Q of the equatoi 
it is noon to this observer. The sun is on his meridian. Six hours 
before this time the sun will rise to him; six hours after he will 
Set. It requires twenty- four hours for the point V to be apparently 
carried all round the equator, and the sun appears to go with the 
point. Three months later the sun is about 90° of right ascension 
and has a north-polar distance of 66^°. The student can determine 
in the same way the circumstances under which the sun will appear 
to him to move on the 21st of next June when its north-polar distance 
is 66i°. 

The example that is here given is not for the purpose of teaching 
the student what the motion of the sun is; that will be considered in 
its proper order in this book. But it is to show him that if he wishes 
to know about it he can find out for himself. 

When he reads about the midnight sun that is visible in the Arctic 
regions he can verify the facts for himself. Let him construct the 
diagram we have described for a place whose latitude is 80° north 
and see what sort of a diurnal orbit the sun will describe on the 21st 
of June when its N. P. D. is 66i°. 

Relation or Time to the Sphere. 

Sidereal Time. — The earth rotates uniformly on its axis; 
that is, it turns through equal angles in equal intervals of 
time. 

This rotation can be used to measure any intervals of 
time when once a unit of time is agreed upon. The most 
natural and convenient unit is a day. There are various 
kinds of days, and we have to take them as they are. 

A sidereal day is the interval of time required for the 
earth to rotate once on its axis. Or what is the same thing, 
it is the interval of time between two consecutive tran- 
sits of any star over the same celestial meridian. The 
sidereal day is divided into 24 sidereal hours; each hour is 
divided into 60 minutes; each minute into 60 seconds. In 
making one revolution the earth turns through 360^*, so that 



44 ASTRONOMY. 

24 hours = 360°; also, 

1 hour ==15°; 1° = 4 minutes. 
1 minute = 15'; 1' = 4 seconds. 
1 second = 15"; 1" = 0.066 second. 

When a star is on the celestial meridian of any place its 
hour-angle is zero, by definition (see page 39). It is then 
at its transit or culmination. 

As the earth rotates, the meridian moves away (east- 
wardly) from this star, whose hour-angle continually in- 
creases from 0° to 360°, or from hours to 24 hours. 
Sidereal time can then be directly measured by the hour- 
angle of any star in the heavens which is on the meridian 
at an instant we agree to call sidereal hours. When this 
star has an hour-angle of 90°, the sidereal time is 6 hours; 
when the star has an hour-angle of 180° (and is again on 
the meridian, but invisible unless it is a circumpolar star), it 
is 12 hours ; when its hour-angle is 270°, the sidereal time 
is 18 hours; and, finally, when the star reaches the upper 
meridian again, it is 24 hours or hours. (See Fig. 13, 
where E C WD is the apparent diurnal path of a star in 
the equator. It is on the meridian at C.) 

Instead of choosing a star as the determining point 
whose transit marks sidereal hours, it is found more con- 
venient to select that point in the sky from which the right 
ascensions of stars are counted — the vernal equinox — the 
point V in the figure. The fundamental theorem of si- 
dereal time is: The hour -migle of the vernal equinox, or the 
sidereal time, is equal to the right ascension of the meri- 
dian; that is, GV^Va 

To avoid continual reference to the stars, we set a clock 
so that its hands shall mark hours minutes seconds 



RELATION OF TEE EARTH TO THE HEAVENS. 45 

at the transit of the yernal equinox, and regulate it so that 
its hour-hand revolves once in 24 sidereal hours. Such a 
clock is called a sidereal clock. 

Solar Time. — Time measured by the hour-angle of the 
sun is called t7'ue or appareiit solar time. A71 apparent 
solar day is the interval of time between two consecutive 
transits of the sun over the upper meridian. The instant 
of the transit of the sun over the meridian of any place 
is the apparent noon of that place, or local apparent noon. 

When the sun's hour-angle is 12 hours or 180°, it is 
local apparent midnight. 

The ordinary sun-dial marks apparent solar time. As 
a matter of fact, apparent solar days are not equal. The 
reason for this will be fully explained later. Hence our 
clocks are not made to keep this kind of time, for if once 
set right they would sometimes lose and sometimes gain 
on such time. 

ICean Solar Time. — A modified kind of solar time is 
therefore used, called mean solar time. This is the time 
kept by ordinary watches and clocks. It is sometimes 
called civil time. Mean solar time is measured by the hour- 
angle of the mean sun, a fictitious body which is imagined 
to move uniformly in the heavens. The law according to 
which the mean sun is supposed to move enables us to com- 
pute its exact position in the heavens at any instant, and to 
define this position by the two co-ordinates right ascension 
and declination. Thus we know the position of this imagi- 
nary body just as we know the position of a star whose 
co-ordinates are given, and we may speak of its transit as 
if it were a bright material point in the sky. A mean 
solar day is the interval of time between two consecutive 
transits of the mean sun over the upper meridian. Mean 



46 ASTRONOMY. 

noon at any place on the earth is the instant of the mean 
sun's transit over the meridian of that place. Twelve hours 
after local mean noon is local mean midnight. The mean 
solar day is divided into 24 hours of 60 minutes each. Each 
minute of mean time contains 60 mean solar seconds. 
Astronomers begin the mean solar day at noon, which is 
hours, and count round to 24 hours. 

We have thus three kinds of time. They are alike in one point: 
each is measured by the hour-angle of some body, real or assumed. 
The body chosen determines the kind of time, and the absolute length 
of the unit — the day. The simplest unit is that determined by the 
uniformly rotating earth — the sidereal day; the most natural unit is 
that determined by the sun itself — the apparent solar day, "which, 
however, is a variable unit; the most convenient unit is the mean 
solar day, and this is the one chosen for use in our daily life. 

Comparative Lengths of the Mean Solar and Sidereal 

Day. — As a fact of observation, it is found that the sun 
appears to move from west to east among the stars, about 
1° daily, making a complete revolution around the sphere 
in a year. It requires 365^ days to move through 360°. 

Hence an apparent solar day will be longer than a side- 
real day. For suppose the sun to be at the vernal equinox 
exactly at sidereal noon (0 hours) of Washington time on 
March 21st; that is, the vernal equinox and the sun are 
both on the meridian of Washington at the same instant. 
In 24 sidereal hours the vernal equinox will again be on the 
same meridian, but the sun will have moved eastwardly by 
about a degree, and the earth will have to turn through 
this angle and a little more in order that the sun shall 
again be on the Washington meridian, or in order that it 
may be apparent noon on March 22d. For the meridian 
-to overtake the sun requires about 4 minutes of sidereal 



RELATION OF THE EARTH TO THE HEAVENS. 47 

time. The true sun does not move, as we have said, uni- 
formly. The mean sun is su|)posed to move uniformly, 
and to make the circuit of the heavens in the same time as 
the real sun. Hence a mean solar day will also be longer 
than a sidereal day, for the same reason that the apparent 
solar day is longer. The exact relation is: 

1 sidereal day = 0-997 mean solar day, 

24 sidereal hours = 23*^ 56°^ 4' -091 mean solar time, 

1 mean solar day = 1-003 sidereal days, 

24 mean solar hours = 24'' 3"* 56^-555 sidereal time, 

and 

366-24222 sidereal days = 365-24222 mean solar days. 

Local Time. — When the mean sun is on the meridian of 
a place, as Boston, it is mean noon at Boston. When the 
mean sun is on the meridian of St. Louis, it is mean noon 
at St. Louis. St. Louis being west of Boston, and the 
earth rotating from west to east, the local noon of Boston 
occurs before the local noon at St. Louis. In the same 
way the local sidereal time at Boston at any given instant 
is expressed by a larger numler than the local sidereal time 
of St. Louis at that instant. 

The sidereal time of mean noon is given in the astro- 
nomical ephemeris for every day of the year. It can be 
found within ten or twelve minutes at any time by remem- 
bering that on March 21st it is sidereal hours about 
noon, on April 21st it is about two hours sidereal time at 
noon, and so on through the year. Thus, by adding two 
hours for each month, and four minutes for each day after 
the 2 1st day last preceding, we have the sidereal time at 
the noon we require. Adding to it the number of hours 
since noon, and one minute more for every fourth of a day 



48 ASTRONOMY. 

on account of the constant gain of the clock (4™ daily), we 
have the sidereal time at any moment. 

Example. — Find the sidereal time on July 4tli, 1881, at 4 o'clock 
A.M. We have: 

h m 

June 21st, 3 mouths after March 21st; to be X 2, 6 

July 3d, 12 days after June 21st; X 4, 48 

4 A.M., 16 hours after noon, nearly | of a day, 16 3 



22 51 

This result is within a minute of the exact value. 

Relation of Time and Longitude. — Considering our civil 
time which depends on the sun, it will be seen that it is 
noon at any and every place on the earth when the sun 
crosses the meridian of that place, or, to speak with more 
precision, when the meridian of the place passes under the 
sun. In the lapse of 24 hours the rotation of the earth on 
its axis brings all its meridians under the sun in succession, 
or, which is the same thing, the sun appears to pass in suc- 
cession over all the meridians of the earth. Hence noon 
continually travels westward at the rate of 15° in an hour, 
making the circuit of the earth in 24 hours. The differ- 
ence between the time of day, or the local time as it is called, 
at any two places will be in proportion to their difference 
of longitude, amounting to one hour for every 15 degrees of 
longitude, four minutes for every degree, and so on. Vice 
versa, if at the same real moment of time we can deter- 
mine the local times at two different places, the difference 
of these times multiplied by 15 will give the difference of 
longitude. 

The longitudes of places are determined astronomically 
on this principle. Astronomers are, however, in the habit 
of expressing the longitude of places on the earth like the 



RELATION OF THE j^xtRTH TO THE HEAVENS. 49 

right ascensions of the heavenly bodies, not in degrees, but 
in hours. For instance, instead of saying that Washington 
is 77° 3' west of Greenwich, we commonly say that it is 5 
hours 8 minutes 12 seconds west, meaning that when it is 
noon at Washington it is 5 hours 8 minutes 12 seconds 
after noon at Greenwich. This course is adopted to prevent 
the trouble and confusion which might arise from constantly 
having to change hours into degrees and the reverse. 

Where does the Day Change? — A question frequently 
asked in this connection is. Where does the day change? 
It is, we will suppose, Sunday noon at Washington. That 
noon travels all the way round the earth, and when it gets 
back to Washington again it is Monday. Where or when 
did it change from Sunday to Monday ? We answer, 
wherever people choose to make the change. Navigators 
make the change occur in longitude 180° from Greenwich. 
As this meridian lies in the Pacific Ocean, and meets 
scarcely any land through its course, it is very convenient for 
this purpose. If its use were universal, the day in question 
would be Sunday to all the inhabitants east of this line, and 
Monday to every one west of it. But in practice there have 
been some deviations. As a general rale, on those islands 
of the Pacific which were settled by men travelling east the 
day would at first be called Monday, even though they 
might cross the meridian of 180°. Indeed the Eussian 
settlers carried their count into Alaska, so that when our 
people took possession of that territory they found that 
the inhabitants called the day Monday when they them- 
selves called it Sunday. These deviations have, however, 
almost entirely disappeared, and with few exceptions the 
day is changed by common consent jn longitude 180° from 
Greenwich. 



50 ASTUOJSOMY. 

Determinations of Terrestrial Longitudes. 

Owing to the rotiition of the earth, there is no such fixed 
correspondence between meridians on the earth and among 
the stars as there is between latitude on the earth and de- 
clination in the heavens. The observer can always deter- 
mine his latitude by finding the declination of his zenith, 
but he cannot find his longitude from the right ascension 
of his zenith with the same facility, because that right as- 
cension is constantly changing. To determine the longi- 
tude of a place, the element of time as measured by the 
diurnal motion of the earth necessarily comes in. Con- 
sider the plane of the meridian of a place extended out to 
the celestial sphere so as to mark out on the latter the 
celestial meridian of the place. Take two such places, 
Washington and San Francisco for example; then there 
will be two such celestial meridians cutting the celes- 
tial sphere so as to make an angle of about forty-five de- 
grees with each other in this case. Let the observer imagine 
himself at San Francisco. Then he may conceive the 
meridian of Washington to be visible on the celestial sphere, 
and to extend from the pole over toward his south-east 
horizon so as to pass at a distance of about forty-five degrees 
east of his own meridian. It would appear to him to be at 
rest, although really both his own meridian and that of 
Washington are moving in consequence of the earth's rota- 
tion. Apparently the stars in their course will first pass 
the meridian of Washington, and about three hours later 
will pass his own meridian. Now it is evident that if he 
can determine the interval which the star requires to pass 
from the meridian of Washington to that of his own place, 
he wiU at p4ce have the difTerence of longitude of the two 



BELATION OF TJIE EARTH TO THE HEAVENS. 51 

places by simply turning the interval in time into degrees 
at the rate of fifteen degrees to each hour. 




Fig. 14. 



The difference of longitude between any two places de- 
pends upon the angular distance of the terrestrial (or celes- 
tial) meridians of these two places and not upon the motion 
of the star or sun which is used to determine this angular 
difference, and hence the longitude of a place is the same 
whether expressed as the difference of two sidereal or of 
two solar times. The longitude of Washington west from 
Greenwich is 5^ S'" or 77°, and this is in fact the ratio of 
the angular distance of the meridian of Washington from 
that of Greenwich, to 24 hours or 360°. The angle between 
the two meridians is ^^^ of 24 hours, or of a whole circum- 
ference, 



52 ASTRONOMY. 

It is thus plain that the difference of longitude of any tiuo 
places is the same as the difference of tlieir si^nultaneous 
local times ; and this whether the local times spoken of 
are both sidereal or both solar. 

Methods of Determining the Difference of Longi- 
tude OF Two Places on the Earth. 

Every purely astronomical method depends upon the 
principle we have just laid down. 

It is of vital importance to seamen to be able to deter- 
mine the longitude of their vessels. The voyage from Liv- 
erpool to New York is made weekly by scores of steamers, 
and the safety of the voyage depends upon the certainty 
with which the captain can mark the longitude and lati- 
tude of his vessel upon the chart. 

The method used by a sailor is this : with a sextant (see 
Chapter III.) the local time of the ship's position is deter- 
mined by an observation of the sun. That is, on a given 
day he can set his watch so that its liands point to twelve 
hours when the sun is on his meridian on that day. He 
carries a chronometer (which is merely a very fine watch) 
whose hands point always to Greenwich time. Suppose 
that when the ship's time is 0^ or noon the Greenwich 
time is 3^^ 20"^. Evidently he is west of Greenwich 3^ ^0^, 
since that is the difference of the simultaneous local times^ 
and since the Greenwich time is later. Hence he is some- 
where on the meridian of 50° west. If he has determined 
the altitude of the pole or the declination of his zenith in 
any way, then he has his latitude also. If this should be 
45° north, the ship is in the regular track between New 
York and Liverpool, and he can go on with safety. 



RELATION OF THE EARTH TO THE HEAVENS. 53 

When the steamer Faraday was laying the direct cable she got her 
longitude every day by comparing her ship's time (found by obser- 
vation on board) with the Greenwich time telegraphed along the cable 
and received at the end of it which she had on her deck. Longitudes 
may be determined in the same way on shore. 

From an observatory, as Washington, the beats of a clock are sent 
out by telegraph along the lines of railway; at every railway station 
and telegraph office the telegraph sounder beats the seconds of the 
Washington clock. Any one who can set his watch to the local time 
of his station and who can compare it with the signals of the Wash- 
ington clock (which are sent at Washington noon, daily except Sun-, 
day) can determine for himself the difference of the simultaneous 
local times of Washington and of his station, and thus his own longi- 
tude east or west from Washington. 



Methods of Determining the Latitude of a Place 
ON THE Earth. 

Latitude from Circumpolar Stars. — In the figure sup- 
pose Z io be the zenith of the observer, H Z RN his me- 




FiG. 15. 



ridiau, P the north pole, H R his horizon. Suj^pose /S'and 
8' to be the two points where a circumpolar star crosses 
the meridian, as it moyes around the pole in its appareut 



54 



ASTRONOMY. 



diurnal orbit. PS 
tance, and P H — q) 

ZS+ZS' 



PS' is the star's north-polar dis- 
the observer's latitude. 



2 



Therefore 



^ = 90° - 



=^ ZP = 90° 

ZS^ZS' 



cp. 



2 



We can measure ZS and ZS', the zenith distances of the 
star in the two positions, by the meridian circle or by the 
sextant, as will be explained in the next chapter. Hence 
having these zenith distances Ave have the latitude of the 
place. 

Latitude by the Meridian Altitude of the Sun or a Star. 
— In the figure let Z be the observer's zenith, P the pole, 

and Q the intersection of 
the celestial equator with the 
meridian H Z H. The alti- 
tude of the star S is meas- 
ured when the star is on the 
meridian. It is known to 
be on the meridian when we 
find its altitude to be a max- 
FiG- 16. imum. From the measured 

altitude of the star S we deduce its zenith distance ZS = <? 
= 90°— II S. Its declination is taken from a catalogue of 
stars if it is a star, or from the Nautical Almanac if it is 
the sun. In either case the declination Q S is known. 

ZQ=QS^-ZS; 

If the body culminates north of the zenith ?it S' , 
ZQ=QS' - ZS', 
cp= d — ^, 




RELATION OF TBE BARTB TO THE BEAVENB. 55 

This is the method uniformly employed at sea, where the 
altitude of the sun at apparent noon is daily measured. 



Parallaxes and Semidiameters of the Heavenly 
Bodies. 

The apparent position of a body on the celestial sphere 
remains the same as long as the observer is fixed, as has 
been shown (see page ?.0). If the observer changes his 
place and the star remains in the same position, the ap- 




FiG. 17. 

parent position of the star will change. To show this let 
CH' be the earth, C being its centre. 8' and ;S'" are the 
places of two observers on the surface. Z' and Z" are 
their zeniths in the celestial sphere H' P" . P is a- star. 
8' will see P in the apparent position P'. 8" will see P 
in the apparent position P". That is, two different ob- 
servers see the same object in two different -apparent 
positions. If the observer xS" moves along the surface 
directly to 8", the apparent position of P on the celes- 
tial sphere will appear to move from P' to P". 
This change is due to the ^mrallax of P. 



56 ASTRONOMY. 

The parallax of a hody due to a change in the position 
of the observer, is the alteration in the apparent position 
of the body catcsed by that change. 

If the observer at 8* could move to the centre of the 
earth along the line B'C, the apparent position of P would 
move from P* to P^. If the observer at 8" could move 
from 8" to C along 8"Cy the apparent position of P would 
move from P" to P ^. 

In the triangle P 8' C the following parts are known: 

C P = A = the geocentric distance of P, 
C 8' = p' = the radius of the earth at 8', 

and the angle 8' PC = P'PP, is i^ke parallax of P. 

For the change of apparent position of P from P' to P^ 
is due to the change of the point of observation from 8' to 

a 

Similarly the angle 8" PC = P"PP, is the parallax of P 
relative to a change of the observer fiom 8" to C. 

Horizontal Parallax. — Clearly the parallax of P differs 
for observers differently situated on the earth, and it is 
necessary to take some standard parallax for each observer. 
Such a standard is the horizontal parallax. Suppose P 
to be in the horizon of the observer 8^', then Z'8'P 
will be 90°, as will also the angle P8'C In the triangle 
8' PC three parts will then be known and the horizontal 
parallax (the angle at P when P is in the horizon) can be 
found. It will be the same for the observer at 8". When 
P is in the horizon of 8" , Z"8"P is a right angle, as is also 
P8"C. C P and C 8" are known and thus the horizontal 
parallax of P is determined. 

If G P, the distance of P, increases, other things remain- 
ing the same, the parallax of P will diminish. 



MeLaTiO]^ Of tSM MABfit TO ¥M reavjsM 5t 

The student can prove this for himself by di'awing the 
figure on the same scale as here given, nutking CP larger. 

The angles at P (the parallaxes) will become smaller and 
Smaller the larger C'P is taken. Hence the magnitude of 
the parallax of a star or a planet depends upon its distance 
from us. 

Suppose an observer at the point F looking at the earth's 
radius S'C. The angle subtended by that semidiameter 
is the same as the parallax of P, Hence we may say that 
the parallax of a body with reference to a?i observer on the 
earth is 7neasured by the angle subtended by that semidi- 
ameter of the earth tuhich passes through the observers 
station. 

As the point P is carried further and further away from 
the earth, the angle subtended by >S" C, for example, becomes 
less and less. If P were at the distance of the moon, this 
angle would be about 57'; if at the distance of the sun, 
it would be about ^". S'C is roughly 4000 miles; it 
subtends an angle of 57' at the distance of the moon. 70 
miles would subtend an angle of about 1', and 3437' 
would be about 240,000 miles. This is the distance of the 
moon from the earth. (See pages 4, 5.) 

Again, 4000 miles subtends an angle of 8". 5 at the dis- 
tance of the sun. 470. 7 miles vv^ould subtend an angle of 
1", and 206,264^8 would be 97,000,000 miles, and this is 
about the distance of the sun. By taking the exact values 
of the radius of the earth and of the solar parallax, this dis- 
tance is found to be about 93,000,000 miles. 

The example shows the method of calculating the sun's 
distance when we have two things accurately given: first, 
the dimensions of the earth; and second, the parallax c£ 
the sun. 

r ^ 



58 ASTRONOMT 

Annual Parallax. — We have seen that for the moon the 
parallax is about 1°; for the sun it is only 8"; for some Df 
the more distant planets it is considerably less. 

For Jupiter it is about 2^^; for Saturn less than 1*; for 
Neptune about 0".3. 

Let us remember what this means. It means that 4000 
miles, the earth's radius, would subtend at the distance of 
Neptune an angle of only y^ of a single second of arc. 

The parallax of the moon is determined by observation, 
and the observations consist in measuring the angle which 
the radius of the earth would subtend if viewed from the 
moon's centre. 57' is an angle large enough to be deter- 
mined quite accurately in this way. There would be but a 
small per cent of error. Even 8", the sun's parallax, can be 
measured so as to have an error of not more than 2 or 3 
per cent. 

But this method will not do to measure anything much 
smaller than S*". The parallax of a fixed star, for example, 
is not ^"ooVfo P^^^ ^s large as the sun's parallax: and this 
is too minute a quantity to be deduced by these methods. 
We therefore use for distant bodies a parallax which does 
not depend on the radius of the earth, but upon the radius 
of the earth's orlit around the sun. 

Tlie annual parallax of a body is tlie angle subtended at 
the body by the radius of the earth^s orbit seen at right 
angles. 

For example, in Fig. 18 suppose that C now represents 
the sun, around which the earth 8' moves in the nearly 
circular orbit 8'8"H'.. S'Cis no longer 4000 miles as in 
the last example, but it is 93,000,000 miles. Suppose F to 
be, again, a body whose annual p)arallax is 8^P C (suppos- 
ing P8'Cto be a right angle). 



HELATION OF TEE EARTH TO THE HEAVENS. 59 



Some of the nearest fixed stars liaye an annual parallax 
of nearly 1". Hence the nearest of them are not nearer 
than 206,264 times 93,000,000 miles. The greater number 
of them have a parallax of not more than -f^". 

Hence their distances cannot be less than 

10 X 206,264 X 93,000,000 miles. 

To the student who has understood the simple rules given 
on pages 4 and 5 these deductions will be plain. 




Fig. 18. 

Semidiameters of the Heavenly Bodies. — The angular 
semidiameter of the sun as seen from the earth is 961". 
Hence its diameter is 1922". Its real diameter in miles is 
therefore about 880,000, as its distance is 93,000,000 miles. 

The angular semidiameter of the moon as seen from the 
earth is about 15^'. Hence its real diameter is about 2000 
miles, its distance being about 240,000 miles. 

In the same way, knowing the distance of any planet and 
measuring its angular semidiameter, we can compute its 
dimensions in miles. 



CHAPTER III 
ASTRONOMICAL INSTRUMENTS. 

General Account. — In a general way we may divide the 
instruments of astronomy into two classes, seeing instru- 
ments and measuring instruments. 

The seeing instruments are telescopes ; they have for 
their object either to enable the observer to see faint objects 
as comets or small stars, or to enable him to see brighter 
stars with greater precision than he could otherwise do. 
How they accomplish this we shall shortly explain. The 
measuring instruments are of two classes. The first class 
measures intervals of time. The second measures angles. 
A clock is a familiar example of the first class; a divided 
circle of the second. 

Let us take these in the order named. 

The Refracting Telescope. — The refracting telescope is 
composed of two essential parts, the object-glass or ohjec- 
tive and the eye-piece. 

The object-glass is for the sole purpose of collecting the 
rays of light which emanate from the thing looked at, and 
for making an image of this thing at a point which is called 
i\iQ focus of the objective. 

The eye-piece has for its sole object to magnify the image 
so that the angular dimensions of the thing looked at will 
appear greater when the telescope is used than when it is 
not. 



ASTRONOMICAL INSTRUMENTS. 



61 



For example, in the figure suppose BI to 
be a luminous surface. Every point of it is 
throwing off rays of light in straight lines in 
every possible direction. Let us consider the 
point /. The rays from / proceed in every 
direction in which we can draw a straight line 
through /. Suppose all such straight lines 
drawn. Let 00' be the odjective of a tele- 
scope pointed towards BI. All the rays from 
/ which fall on 00' lie between the lines 10^ 
and 10'. No others can reach the objective, 
and all others which proceed from / are 
wasted so far as seeing / with this particu- 
lar telescope is concerned. 

The action of the convex lens 00' is to 
bend every ray which passes through it to- 
wards its axis BA. TO is bent down to 01' \ 
10' is bent up to O'l'-, and so for every 
other ray except the ray from / through the 
centre of 00' which is bent neither up nor 
down, but which goes straight on to /'and 
beyond. 

Every one of the rays of light sent out by 
/ between the limits 10 and 10' finally passes 
through /'. / is a point of light, and so is 
/'. The point /' is the focus of 00' with 
respect to /. 

Similarly B sends out light in every direc- 
tion. Only those rays which chance to fall 
between BO and BO' are useful for seeing 
jSwith this particular telescope. Everyone 
of this bundle of rays comes to a, focus on the 



Fia, 19« 



62 ASTRONOMY. 

intersection of the lines /' and BA. In tlie same way 

every point of the olject BI has a corresponding image on 

the line /' somewhere between /' and the axis BA, 

I' is the focal plane of the objective with respect to 

the object BI, and the image of BI lies in this focal plane. 
The objective has now done all it can; it has gathered 
every possible ray from the object BI and presents every 
one of these rays concentrated in an image of this object 
in the focal plane at /' 

Notice two things: first, the image is inverted with re- 
spect to the object; /is above B\ the image of / is below 

the image of' B\ second, the rays from B /do not 

stop at /' , but go on indefinitely to the left, always 

diverging from the image. 

The Eye-piece. — The eye-piece is essentially a microscope 
which is simply to magnify the angular dimensions of the 
object as it is seen in the telescope; that is, to magnify the 
image. To see well with a microscope it must be close to 
the thing magnified. It cannot be placed near to BI in 
general, for BI may be a mile or ten millions of miles 
away. So the place to put it is near to the image of BI, a 
little above the focal plane /' in the figure. 

The eye must be placed a little further above still, 
at such a position as to see well with the eye-piece. That 
is, close to it. Now fix an objective in one end of a tube 
and an eye-piece in the other end and you have a refracting 
telescope. The more powerful the microscope used as an 
eye-piece the higher the magnifying power of the combina- 
tion. We increase the magnifying power of any telescope 
by changing the eye-piece. . 

The Objective. — As a matter of fact the objective is usu- 
ally made of two glasses like the figure, where the arrow 




ASTRONOMICAL INSTRUMENTS. 63 

shows the direction in which the rays come to it from the 
object. If we use a single ob- 
jective we find that the image of 
the object is colored ; that is, of 
different colors from its natural 
tints. We find that by using a 
double objective made of two fig. 20. 

different kinds of glass this can be corrected. This is ex- 
plained in Optics under the head of Achromatism or Chro- 
matic Aberration. 

Light-gathering Power. — It is not merely by magnifying 
that the telescope assists the vision, but also by increasing 
the quantity of light which reaches the eye from the object 
at which we look. Indeed, should we view an object 
through an instrument which magnified but did not in- 
crease the amount of light received by the eye, it is evident 
that the brilliancy would be diminished in proportion as 
the surface of the image Avas enlarged, since a constant 
amount of light would be spread over an increased surface; 
and thus, unless the light were very bright, the object might 
become so darkened as to be less plainly seen than with the 
naked eye. How the telescope increases the quantity of 
light will be seen by considering that when the unaided 
eye looks at any object, the retina can only receive so many 
rays as fall upon the pupil of the eye. By the use of the 
telescope it is evident that as many rays can be brought to 
the retina as fall on the entire object-glass. The pupil of 
the human eye, in its normal state, has a diameter of about 
one fifth of an inch, and by the use of the telescope it is 
virtually increased in surface in the ratio of the square of 
the diameter of the objective to the square of one fifth of 
an inch^ that is, in the ratio of the surface of the objective 



64 ASTRONOMY. 

to the surface of the pupil of the eye. Thus, with a two- 
inch aperture to our telescope, the number of rays collected 
is one hundred times as great as the number collected with 
the naked eye. 

With a 5-inch object-glass the ratio is 625 to 1 
" 10 " " " " 2,500 to 1 

** 15 " " " " 5,625 to 1 

" 20 '* ** " '' 10,000 to 1 

" 26 " ** " " 16,900 to 1 

When a minute object, like a small star, is viewed, it is 
necessary that a certain number of rays should fall on the 
retina in order that the star may be visible at all. It is 
therefore plain that the use of the telescope enables an 
observer to see much fainter stars than he could detect with 
the naked eye, and also to see faint objects much better 
than by unaided vision alone. Thus, with a 26-inch tele- 
scope we may see stars so minute that it would require the 
collective light of many thousands to be visible to the 
unaided eye. 

Eye-piece. — In the skeleton form of telescope before de- 
scribed the eye-piece as well as the objective was considered 
as consisting of but a single lens. But with such an eye- 
piece vision is imperfect, except in the centre of the field, 
from the fact that the image does not throw rays in every 
direction, but only in straight lines away from the objec- 
tive. Hence the rays from near the edges of the focal 
image fall on or near the edge of the eye-piece, whence 
arises distortion of the image formed on the retina, and loss 
of light. To remedy this difficulty a lens is inserted at or 
very near the place where the focal image is formed, for the 
purpose of throwing the different pencils of rays which 
§manate from the several parts of the image, toward the 



ASTRONOMICAL INSTRUMENTS. 65 

axis of the telescope, so that they shall all pass nearly 
through the centre of the eye-lens proper. These tv/o 
lenses are together called the eye-piece. 

There are some small differences of detail in the con- 
struction of eye-pieces^ but the general principle is the 
same in all. 

The figure shows an eye-piece drawn accurately to scale. 0/is 
one of the converging pencils from the object-glass which forms one 
point (/) of the focal image la. This image is viewed by the field- 
lens F of the eye-piece as if it were a real object, and the shaded pencil 
between i^and ^sliows the course of these rays after deviation hy F. 
If there were no eye-lens E, an eye properly placed beyond ^ would 
see an image at I a'. The eye-lens £^ receives the pencil of rays, and 
deviates it to the observer's eye placed at such a point that the whole 
incident pencil will pass through the pupil and fall on the retina, and 
thus be effective. As we saw in the figure of the refracting telescope, 




Fio. 21. 

every point of the object produces a pencil similar to 07, and the 
whole surfaces of the lenses i^and J^are covered with rays. All of 
these pencils passing through the pupil go to make up the retinal 
image. This image is referred by the mind to the distance of distinct 
vision (about ten inches), and the image AI" represents the dimen- 
sion of the final image relative to the image al as formed by the ob- 

A I' 
jective, and — — is evidently the magnifying power of this particulai 

^ye-piece used in combination with this particular objective, 



66 ASTRONOMY. 

Reflecting Telescopes. — As we have seen, one essential part of a 
refracting telescope is the objective, which brings all the incident rays 
from an object to one focus, forming there an image of that object. 
In reflecting telescopes (reflectors) the objective is a mirror of specu- 
lum metal or silvered glass ground to the shape of a paraboloid. The 
figure shows the action of such a mirror on a bundle of parallel rays^ 
which, after impinging on it, are brought by reflection to one focus 
F. The image formed at this focus may be viewed with an eye- 
piece, as in the case of the refracting telescope. 

The eye-pieces used with such a mirror are of the kind already 
described. lu the figure the eye-piece would have to be placed to 




Fig, 



the right of the point F, and the observer's head would thus interfere 
with the incident light. Various devices have been proposed to rem- 
edy this inconvenience, of which the most simple is to interpose a 
small plane mirror, which is inclined 45° to the line AC, just to the 
left of F. This mirror will reflect the rays which are moving towards 
the focus i^down (in the figure) to another focus outside of the main 
beam of rays. At this second focus the ej^e-piece is placed and the 
observer looks into it in a direction perpendicular to AG. 

The Telescope in Measurement. — A telescope is generally 
thought of only as an instrument to assist the eye hy its 
magnifying and light-gathering power in the manner we 
have described. But it has a very important additional 
function in astronomical measurements by enabling the 
astronomer to point at a celestial object with a certainty 
and accuracy otherwise unattainalle. This function of 
the telescope was not recognized for more than half a cen- 



ASTRONOMICAL INSTRUMENTS. 67 

tury after its invention, and after a long and rather acri- 
monious contest between two schools of astronomers. 
Until the middle of the seventeenth century, when an 
astronomer wished to determine the altitude of a celestial 
object, or to measure the angular distance between two 
stars, he was obliged to point his sextant or other meas- 
uring instrument at the object by means of ** pinnules." 
These served the same purpose as the sights on a rifle. In 
using them, however, a difficulty arose. It was impossible 
for the observer to have distinct vision both of the object 
and of the pinnules at the same time, because when the 
eye was focused on either pinnule, or on the object, it was 
necessarily out of focus for the others. The only way to 
diminish this difficulty was to lengthen the arm on which 
the pinnules were fastened so that the latter should be as 
far apart as possible. Thus Tycho Brahe, before the 
year 1600, had measuring instruments very much larger 
than any in use at the present time. But this plan only 
diminished the difficulty and could not entirely obviate it, 
because to be manageable the instrument must not be very 
large. 

About 1670 the English and French astronomers found 
that by simply inserting fine threads or wires exactly in 
the focus of the object-glass, and then pointing it at the 
object, the image of that object formed in the focus could 
be made to coincide with the threads, so that the observer 
could see the two exactly superimposed upon each other. 
When thus brought into coincidence, it was obvious that 
the point of the object on which the wires were set was in 
a straight line passing through the wires, and through the 
centre of the object-glass. So exactly could such a point- 
ing be made, that if the telescope did not magnify at all 



68 ASTB0N0M7, 

(the eye-piece and object-glass being of equal focal length), 
a very important advance would still be made in the ac- 
curacy of astronomical measurements. This line, passing 
centrally through the telescope, we call the line of coUi- 
mation of the telescope, ^ ^ in Fig. 19. If we have any 
way of determining it, it is as if we had an indefinitely long 
pencil extended from the earth to the sky. If the observer 
simply sets his telescope in a fixed position, looks through 
it and notices what stars pass along the threads in the eye- 
piece, he knows that all those stars lie in the axis of col- 
limation of his telescope at that instant 

By the diurnal motion a pencil-mark, as it were, is thus 
drawn on the surface of the celestial sphere among the 
stars, and the direction of this pencil-mark can be deter- 
mined with far greater precision by the telescope than with 
the naked eye. 

Chronometers and Clocks, 

We have seen that it is important for various purposes 
that an observer should be able to determine his local time 
(see page 52). This local time is determined most accu- 
rately by observing the transits of stars over the celestial 
meridian of the place where the observer is. In order to 
determine the moment of transit with all required accuracy, 
it is necessary that the time-pieces by which it is measured 
shall go with the greatest possible precision. There is no 
great difficulty in making astronomical measures to a sec- 
ond of arc, and a star, by its diurnal motion, passes over 
this space in one fifteenth of a second of time (see page 
41:). It is therefore desirable that the astronomical clock 
shall not vary from a uniform rate more than a few 



ASTRONOMICAL INSTRUMENTS. 6.9 

hundredths of a second in the course of a day. It is 
not, however, necessary that it should always be perfectly 
correct; it may go too fast or too slow without detracting 
fi'om its character for accuracy, if the interyals of time 
which it tells off — hours, minutes, or seconds — are always 
of exactly the same length, or, in other words, if it gains 
or loses exactly the same amount every hour and every 
day. 

The time-pieces used in astronomical observation are the 
chronometer and the clock. 

The chronometer is merely a very perfect watch with 
a balance-wheel so constructed that changes of tempera- 
ture have the least possible effect upon the time of its 
oscillation. Such a balance is called a compe^isation bal- 
ance. 

The ordinary house-clock goes faster in cold than in 
warm weather, because the pendulum-rod shortens under 
the influence of cold. This effect is such that the clock 
will gain about one second a day for every fall of 3° Cent. 
(5°. 4 Fahr.) in the temperature, supposing the pendulum- 
rod to be of iron. Such changes of rate would be entirely 
inadmissible in a clock used for astronomical purposes. 
The astronomical clock is therefore provided with a com- 
pensation pendulum, by which the disturbing effects of 
changes of temperature are avoided. 

The correction of a clock is the quantity which it is necessary to 
add to the indications of the hands to obtain the true time. Thus if 
the correction of a sidereal clocli is + 1"" 10^07 and the hands point 
to 21^ 13"" 14».50, the correct sidereal time is ^V" 14°^ 24'. 57. 

The rate of a clock is the daily change of its correction; i.e., what 
it gains or loses daily. 



70 



ASTRONOMY, 



The Transit Instrument. 

Tlie Transit Instrument is used to observe the traiKsits 
of stars over the celestial meridian. The times of these 




Fig. 23. 



transits are noted by the sidereal clock, which is an indis- 
pensable adjunct of the transit instrument. 



ASmONOMIGAL INSTRXIMENTS. 71 

It consists essentially of a telescope TT mounted on an axis VV 
at right angles to it. The ends of this axis terminate in accurately 
■cylindrical pivots which rest in metallic bearings W which are 
shaped like the letter Y, and hence called the Y's. 

These are fastened to two pillars of stone, brick, or iron. Two 
counterpoises TTTTare connected with the axis as in the plate, so as 
to take a large portion of the weight of the axis and telescope from 
the Y's, and thus to diminish the friction upon these and to render 
the rotation about FF more easy and regular. In the ordinary use 
of the transit, the line F F is placed accurately level and also perpen- 
dicular to the meridian, or in the east and west line. To effect this 
"adjustment" there are two sets of adjusting screws, by which the 
ends of F Fin the Y's may be moved either up and down, or north 
and south. The plate gives the form of transit used in permanent 
observatories, and shows the observing chair C, the reversing carriage 
B, and the level L. The arms of the latter have Y's, which can be 
placed over the pivots FF 

Tlie line of collimaiion of the transit telescope is the line drawn 
through the centre of the objective perpendicular to the rotation 
axis VV. 

The reticle is a network of fine spider-lines placed in the focus of 
the objective. 

In Fig. 24 the circle represents the field of view of a transit as seen 
through the eye-piece. The seven vertical 
lines, I, II, III, IV, Y, VI, VII, are seven 
fine spider -lines tightly stretched across a 
hole in a metal plate, and so adjusted as 
to be perpendicular to the direction of a 
star's apparent diurnal motion. The hori- 
zontal wires, guide-wires, a and h, mark the 
centre of the field. The field is illuminated 
at night by a lamp at the end of the axis 
which shines through the hollow interior of 
the latter, and causes the field to appear 
bright. The wires are dark against a bright 
ground. The line of sight is a line joining the centre of the objective 
and the central one, IV, of the seven vertical wires. 

The whole transit is in adjustment when, first, the axis FF is 
horizontal; second, when it lies east and west; and third, when the 
line of sight and the line of collimation coincide. When these condi- 
tions are fulfilled the line of sight intersects the celestial sphere in the 
meridian of the place, and when T T is rotated about F F the line of 
sight marks out. the celestial meridian of the place on the sphere. 




72 ASTRONOMY. 

The clock stands neur the transit instrnment. The times 
when a star passes the wires I-VII are noted. The average 
of these is the time when the star was on the middle thread, 
or, what is the same thing, on the celestial meridian. At 
that instant its hour-angle is zero. (See page 39.) 

The sidereal time at that instant is the hour-angle of the 
vernal equinox (see page 44). This is measured from the 
meridian towards the west. The right ascension of the 
star which is observed is the same quantity, measured from 
the vernal equinox towards the cast. As the star is on 
the meridian, the two are equal. Suppose we know the 
right ascension of the star and that it is a. Suppose the 
clock time of transit is T. It should have been a if the 
clock were correct. The correction of the clock at this 
instant is thus a — T. 

This is the use we make of stars of Tcnown right ascen- 
sions. By observing any one of them we can get a value of 
the clock correction. 

Suppose the clock to be correct, and suppose we note that 
a star whose right ascension is imhnown is on the wire IV 
at the time a' by the clock, a' is then the right ascension 
of that star. In this way the positions of stars, or of the 
sun and planets (in right ascension only), are determined. 

The Mebidian Circle. 

The meridian circle is a combination of the transit in- 
strument with a graduated circle fastened to its axis and 
moving with it. A meridian circle is shown in Fig. 25. 
It has two circles finely divided on their sides. The grad- 
uation of each circle is viewed by four microscopes. The 
microscopes are 90° apart. The cut shows also the hang- 
ing level by which the error of level of the axis is found. 



ASTRONOMICAL INSTRXIMENTB. 



'73 



The instrument can be used as a transit to determine 
right ascensions, as before described. It can be also used 
to measure declinations in the following way : If the 
telescope is pointed to the nadir, a certain diyision of 




Fig. 25. 



the circles, as N, is under the first microscope. We can 
make the nadir a yisible point by placing a basin of quick- 
silver below the telescope and looking in it through the tel- 
escope. AYe shall see the wires of the reticle and also their 



74 ASTRONOMY. 

reflected images in the quicksilver. When these coincide, 
the telescope points to the nadir. If it is then pointed to 
the pole, the reading will change by the angular distance 
between the nadir and the pole, or by 90° -\- cp, cp being the 
latitude of the place (supposed to be known). The polar 
reading P of the circle is thus known when the nadir 
reading iVis found. If the telescope is then pointed to 
various stars of unknoimi polar distances, p', ^", /j'", etc., 
as they successively cross the meridian, and if the circle 
readings for these stars are P', P", P'", etc., it follows 
that f=P'—P', p'' = P"—P', p'" = P'^' — P', etc. 

Thus the meridian circle serves to determine by observa- 
tion hoth co-ordinates of the apparent position of a body. 

The Equatorial. 

An equatorial telescope is one mounted in such a way that 
a star may be followed through its diurnal orbit by turning 
the telescope about one axis only. The equatorial mount- 
ing consists essentially of a pair of axes at right angles 
to each other. One of these S N {the polar axis) is direct- 
ed toward the elevated pole of the heavens, and it there- 
fore makes an angle with the horizon equal to the latitude 
of the place (p. 31). This axis can be turned about its own 
axial line. On one extremity it carries another axis L D 
(the declination axis), which is fixed at right angles to it, 
but which can again be rotated about its axial line. 

To this last axis a telescope is attached, which may either 
be a reflector or a refractor. It is plain that such a tele- 
scope may be directed to any point of the heavens; for we 
can rotate the declination axis until the telescope points to 
any given polar distance or declination. Then, keeping 
the telescope fixed in respect to the declination axis, we can 



ASTRONOMICAL INSTRUMENTS. 



YlQ. 26. 



•76 ASTRONOMY. 

rotate tlie whole instrument as one mass about the polar 
axis until the telescope points to any portion of the parallel 
of declination defined by the given right ascension or hour- 
angle. Fig. 26 is an equatorial of six-inch aperture which 
can be moved from place to place. 

If we point such a telescope to a star when it is rising (doing this 
by rotating tlie telescope first about its declination axis and then 
about the polar axis), and fix the telescope in this position, we can, 
by simply rotating the whole apparatus on the polar axis, cause the 
telescope to trace out on the celestial sphere the apparent diurnal 
path which this star will appear to follow from rising to setting. In 
such telescopes a driving-clock is so arranged that it can turn the 
telescope round the polar axis at the same rate at which the earth it- 
self turns about its own axis of rotation, but in a contrary direction. 
Hence such a telescope once pointed at a star will continue to point 
at it as long as the driving-clock is in operation, thus enabling the 
astronomer to make such an examination or observation of it as is 
required. 

The Sextant. 

The sextant is a portable instrument by which the altitudes of 
celestial bodies or the angular distances between them may be 
measured. It is used chiefly by navigators for determining the lati- 
tude and the local time of the position of the ship. Knowing the 
local time, and comparing it with a chronometer regulated on Green- 
wich time, the longitude becomes known and the ship's place is 
fixed. (See page 52.) 

It consists of an arc of a divided circle usually 60° in extent, 
whence the name. This arc is in fact divided into 120 equal parts, 
each marked as a degree, and these are again divided into smaller 
spaces, so that by means of the vernier at the end of the index-arm 
MS an arc of 10" (usually) may be read. 

The index-arm MS carries the index-glass M, which is a silvered 
plane mirror set perpendicular to the plane of the divided arc. The 
liorizon-glass m is also a plane mirror fixed perpendicular to the plane 
of the divided circle. 

This last glass is fixed in position, while the first revolves with the 
index-arm. The horizon-glass is divided into two parts, of which 
the lower one is silvered, the upper half being transparent. JS^ is a 
telescope of low power pointed toward the horizon-glass. By it any 



ASTRONOMICAL INSTRUMENTS. 



KK 



object to which it is directly pointed can be seen through the urm-lvered 
half of the horizon -glass. Any other ol)ject in the same plane can be 
brought into the same field by rotating the index-arm (and the index- 
glass with it), so that a beam of light from this second object shall 
strike the index-glass at the proper angle, there to be reflected to the 
horizon-glass, and again reflected down the telescope E. Thus the 
images of any two objects in the plane of the sextant may be brought 
together in the telescope by viewing one directly and the other by 
reflection. 




Fig. 27. 

This instrument is used daily at sea to determine the 
ship's position by measuring the altitude of the sun. This 
is done by pointing the telescope, FB, to the sea-horizon, 
H in the figure, which aj^pears like a line in the field of the 
telescope, and by moving the index-arm till the image of 



78 ASTRONOMY. 

the sun, S, coincides with the horizon. The arc read from 
the sextant at this time is the sun's altitude. From the 
altitude of the sun on the meridian the ship's latitude is 
known (see page 52). From its altitude at another hour 




Fig. 28. 

the local time can be computed. The difference between 
the local time and the Greenwich time, as shown by the 
ship's chronometer, gives the ship's longitude. By means 
of this simple instrument the place of a vessel can be found 
witnin a mile or so. 

The above are the instruments of astronomy which best 
illustrate the principles of astronomical observations. 

Practical Astronomy is the science which teaches the 
theory of these instruments and of their application to ob- 
servation, and it includes the art of so combining the 
observations and so using the appliances as to get the best 
results. 



ASTRONOMICAL EPHEMEBI8. 79 



The Astronomical Ephemeris, or Nautical Almanac. 

The Astronomical Ephemeris, or, as it is more commonly called, 
the Nautical Almanac, is a work iu which celestial phenomena and 
the positions of the heavenly bodies are computed in advance. 

The usefulness of such a work, especially to the navigator, de- 
pends upon its regular appearance on a uniform plan and upon the 
fulness and accuracy of its data; it was therefore necessary that its 
fssue should be taken up as a government work. An astronomical 
ephemeris or nautical almanac is now published annually by each of 
the governments of Germany, Spain, Portugal, France, Great Britain, 
and the United States. They are printed three years or more be- 
forehand, in order that navigators going on long voyages may supply 
themselves in advance. 

The Ephemeris furnishes the fundamental data from which all our 
household almanacs are calculated. 

The principal quantities given in the American Ephemeris for 
each year are as follows: 

The positions (R. A. and d) of the sun and the principal large 
planets for Greenwich noon of every day in each year. 

The right ascension and declination of the moon's centre for every 
Greenwich hour in the year. 

The distance of the moon from certain bright stars and planets for 
every third Greenwich hour of the year. 

The right ascensions and declinations of upward of two hundred 
of the brighter fixed stars, corrected for precession, nutation, and 
aberration, for every ten days. 

The positions of the principal planets at every visible transit over 
the meridian of Washington. 

Complete elements of all the eclipses of the sun and moon, with 
maps showing the passage of the moon's shadow or penumbra over 
those regions of the earth where the eclipses will be visible, and 
tables whereby the phases of the eclipses can be accurately computed 
for any place. 

Tables for predicting the occultations of stars by the moon. 

Eclipses of Jupitefs satellites and miscellaneous phenomena. 

Catalogues of Stars. — Of the same general nature with the Ephe- 
meris are catalogues of the fixed stars. The object of such a cata- 
logue is to give the right ascension and declination of a number of 
stars for some epoch, the beginning of the year 1875 for instance, 
with the data by which the position of each star can be found at any 
other epoch. 



80 



ASTRONOMY. 



To give the student a still further idea of the Epliemeris, we present 
a snaall portion of one of its pages for the year 1882 : 

February, 1883— at Greenwich Mean Noon. 



""oT 


1.- 

ti_, -(.3 






The Sun 


's 




Equation 
of time 
to be 
subtracted 
from 
mean 
time. 


u 

5 


Sidereal 

time 
or right 
ascension 

of 
mean sun. 


the 
weelc- 


Apparent 

right 
ascension. 


Difif. 
fori 
hour. 


Apparent 
declination. 


Diff. 
fori 
hour. 


Wed. 
Thur. 
Frid. 


1 

2 
3 


H. 

21 
21 
21 


M. 


4 
8 


s. 
13.04 
16.84 
19.82 


s. 
10.175 
10.141 
10.107 


o 

S17 
16 
16 


2 
45 

27 


22.4 

5.4 
30.9 


+42.82 
43.57 
44.30 


M. S. 

13 51.34 

13 58.58 

14 5.01 


0.318 
0.284 
0.250 


H. 

20 
20 

20 


M. S. 

46 21.70 
50 18.26 
54 14.81 


Sat. 
Sun. 
Mon. 


4 
5 
6 


21 
21 
21 


12 
16 
20 


21.98 
23.33 

23.88 


10.073 
10.040 
10.007 


16 
15 
15 


9 
51 
33 


39.8 

30.8 

6.1 


+44.99 
45.69 
46.36 


14 10.61 
14 15.41 
14 19.40 


0.216 
0.183 
0.150 


20 
21 
21 


58 11.37 
2 7.92 
6 4.48 


Tues. 
Wed. 
Thur. 


7 
8 
9 


21 
21 
21 


24 

28 
32 


23.63 
22.60 
20.79 


9.974 
9.941 
9.909 


15 
14 
14 


14 
55 
36 


25.4 
29.1 
17.7 


+47.03 
47.66 
48.28 


14 22.60 
14 25.01 
14 26.65 


0.117 
0.084 
0.052 


21 
21 
21 


10 1.03 
13 57.59 
17 54.14 


Frid. 

Sat. 

Sun. 


10 
11 
VZ 


21 
21 
21 


36 
40 
44 


18.21 

14.88 
10.80 


9.877 
9.816 
9.815 


14 
13 
13 


16 
57 
37 


51.6 
11.2 
16.9 


48.88 
49.47 
50.03 


14 27.51 
14 27.63 
14 26.99 


0.020 
0.011 
0.042 


21 
21 
21 


21 50.70 
25 47.25 
29 43.81 


Mon. 
Tues. 
Wed. 


13 
14 
15 


21 
21 
21 


48 
52 
55 


5.98 

0.43 

54.16 


9.784 
9.753 
9.723 


13 
12 
12 


17 
56 
36 


9.1 
48 3 
14.9 


+50.59 
51.12 
51.65 


14 25.63 
14 23.52 
14 20.70 


0.073 
0.104 
0.134 


21 
21 
21 


33 40 35 
37 36.91 
41 33.46 


Thur. 
Frid. 
Sat. 


16 
17 

18 


21 
22 
22 


59 
3 

7 


47.17 
39.47 
31.07 


9.693 
9.664 
9.635 


12 
11 
11 


15 
54 
33 


29.3 
32.1 
23.6 


+52.14 
52.62 
53.07 


14 17.15 
14 12.90 
14 7.94 


0.164 21 
0.193 21 
0.222,21 


45 30.02 
49 26.57 
53 23.13 



The third column shows the R. A. of the sun's centre at Green- 
wich mean noon of each da}'". The fourth column shows the hourly 
change of this quantity (9.815 on Feb. 12). At Greenwich hours 
the sun's R. A. was 21 '^ 44'" 10^80. Washington is S'^ 8"" (5*^.13) 
west of Greenwich. At Washington mean noon, on the 12th, the 
Greenwich mean time was 5\ 13. 9.815 X 5.13 is 50«.35. This is to 
be added, since the R. A. is increasing. The sun's R. A. at Wash- 
ington mean noon is therefore 21^ 45"* 1'.15. A similar process will 
give the sun's declination for Washington mean noon. In the same 
manner, theR. A. and Dec. of the sun for «?i^ place whose longitude 
is known can be found. 

The column "Equation of Time" gives the quantity to be sub- 
tracted from the Greenwich mean solar time to obtain the Green- 
wich apparent solar time (see page 188). Thus, for Feb. 1, the 
Greenwich mean time of Greenwich mean noon is O'* 0"" 0*. The 
true sun crossed the Greenwich meridian (apparent noon) at 23^ 46°* 
08\66 on the preceding day; i.e., Jan. 31. 

When it was 0'' 0™ 6' of (Greenwich mean time on Feb, 13, it was 
also 21'* 33^" 40\35 of Greenwich local sidereal time (see the last 
column of the table). 



CHAPTER IV. 
MOTION OF THE EARTH. 

Ancient Ideas of the Planets. 

It was observed by the ancients that while the great 
mass of the stars maintained their positions relatively to 
each other month after month and year after year, there 
were visible to them seven heavenly bodies which changed 
their positions relatively to the stars and to each other. 
These they called planets or wandering stars. It was found 
that the seven planets performed a very slow revolution 
around the celestial sphere from west to east, in periods 
ranging from one month in the case of the moon to thirty 
years in that of Saturn. 

The idea of the fixed stars being set in a solid sphere was 
in perfect accord with their diurnal revolution as observed 
by the naked eye. But it was not so with the planets. 
The latter, after continued observation, were found to 
move sometimes backward and sometimes forward; and it 
was quite evident that at certain periods they were nearer 
the earth than at other periods. These motions were en- 
tirely inconsistent with the theory that they were fixed in 
solid spheres. 

These planets (which are visible to the naked eye), 
together with the earth, and a number of other bodies 
which the telescope has made known to us, form a family 
or system by themselves, the dimensioiis o| which, altliough 



82 ASTRONOMY. 

inconceivably greater tlian any wliich we have to deal with 
at the surface of the earth, are quite insignificant when 
compared with the distance which separates us from the 
fixed stars. The sun being the great central body of this 
system, it is called the Solar System. There are eight 
large planets, of which the earth is the third in the order of 
distance from the sun, and these bodies all perform a regular 
revolution around the sun. Mercury ^ the nearest, performs 
its revolution in three months ; Ne]^tiine, the farthest, in 
164 years. 

Annual Revolution of the Earth. 

To an observer on the earth the sun seems to perform 
an annual revolution among the stars, a fact which has 
been known from early ages. This motion is due to the 
annual revolution of the earth round the sun. 

In Fig. 29 let S represent the sun, ABGD the orbit 
of the earth around it, and E FGH the sphere of the 
fixed stars. This sphere, being supposed infinitely distant, 
must be considered as infinitely ^larger than the circle 
ABGD, Suppose now that 1, 2, 3, 4, 5, 6 are a number 
of consecutive positions of the earth in its orbit. The line 
IS drawn from the sun to the earth in the first position is 
called the radius-vector of the earth. Suppose this line 
extended infinitely so as to meet the celestial sphere in the 
point 1'. It is evident that to an observer on the earth at 
1 the sun will appear projected on the sphere in the direc- 
tion of 1'; when the earth reaches 2 it will ai')pear in the 
direction of 2', and so on. In other words, as the earth 
revolves around the sun, the latter will seem to perform a 
revolution among the fixed stars, which are immensely 
inore distant than itself. The points 1', 2', etc., can be 



MOTIONS OF THE EARTH. g3 

fixed by their relations to the yarious fixed stars, whose 
places are known. 

It is also evident that the point in which the earth would 
be projected if viewed from the sun is always exactly 
opposite that in which the sun appears as projected from 
the earth. Moreover, if the earth moves more rapidly in 




Fig. 29.— Revolution of the Earth. 



some points of its orbit than in others, it is evident that 
the sun will also appear to move more rapidly among the 
stars, and that the two motions must always accurately 
correspond to each other. 

The r^dius-yector of the earth in its annual course de- 
icribes a plane;, which in the figure may be represented by 



84 ASTRONOMY. 

that of the paper. This plane continued to infinity in 
every direction will cut the celestial sphere in a great cir- 
cle ; and it is clear that the sun will always appear to 
move in this circle. The plane and the circle are indiffer- 
ently termed the ecliptic. The plane of the ecliptic is gen- 
erally taken as the fundamental one, to which the positions 
of all the bodies in the solar system are referred. It 
divides the celestial sphere into two equal parts. In think- 
ing of the celestial motions, it is convenient to conceive of 
this plane as horizontal. Then if we draw a vertical line 
through the sun at right angles to this plane (perpendicular 
to the plane of the paper on which the figure is represent- 
ed), the point at which this line intersects the celestial 
sphere will be the pole of the ecliptic. 

Let us now study the apparent annual revolution of the 
sun produced by the real revolution of the earth in its orbit. 

When the earth is at 1 in the figure the sun will appear 
to be at V, near some star, as drawn. Now by the diurnal 
motion of the earth the sun is made to rise, to culminate, 
and to set successively for each meridian on the globe. This 
star being near the sun rises, culminates, and sets with it; 
it is on the meridian of any place at the local noon of that 
place (and is therefore not visible except in a telescope). The 
star on the right-hand side of the figure near the line C SI 
prolonged is nearly opposite to the sun. When the sun is 
rising at any place, that star will be setting; when the sun 
is on the meridian of the place, this star is on the lower 
meridian; when the sun is setting, this star is rising. It 
is about 180° from the sun. Now suppose the earth to 
move to 2. The sun will be seen at 2', near the star there 
marked. 2' is east of 1'; the sun appears to move among 
ihe stars (in consec^uence of the earth's annual motion^ 



MOTIONS OF THE EARTH. 85 

from west to east. The star near 2' will rise, culminate, 
and set with the sun at every place on the earth. The star 
near 1' being ivest of 2' will rise iefore the sun, culminate 
before him, and set before he does. 

If, for example, the star 1' is near the equator when the 
sun is 15° east of it, the star will rise about 1 hour earlier 
than the sun. When the sun is 30° east of it (at 3', for 
example), the star will rise 2 hours before the sun. When 
the sun is 90° east of 1', the star will rise 6 hours before the 
sun, and so on. That is, when the sun is rising at any- 
place, this star will be on the meridian of the place. When 
the sun appears in the line VCS 1 prolonged to the right 
in the figure, the star 1' will be on the meridian at mid- 
night, and is then said to be in ojjposition to the sun. It 
is 180° from it. When the sun appears to be near H, the 
star V will be about 45° or 3 hours east of the sun. The 
sun will rise first to any place on the earth, and the star 
will rise 3 hours later, say at 9 a.m. Finally the sun will 
come back to the same star again and they will rise, culmi- 
nate, and set together. 

We know that this cycle is about 365 days in length. 
In this time the sun moves 360°, or about 1° daily. This 
cycle is perpetually repeated. Its length is a sidereal year; 
that is, the interval of time required for the sun to move 
in the sky from one star back to the same star again or for 
the earth to make one revolution in its orbit among the 
stars. 

The ancients were familiar with this phenomenon. They 
knew most of the brighter stars by name. The lieliacal 
rising of a bright star (its rising with Helios, the sun) 
marked the beginning of a cycle. At the end of it, seasons 
and crops an(i tbe periodical floods of the Nile had repeat- 



86 ASTRONOMY, 

ed themselves. It was in this way that the first accurate 
notions of the year arose. 

The apparent position of a body as seen from the earth 
is called its geocentric place. The apparent position of a 
body as seen from the sun is called its heliocentric place. 

In the last figure, suppose the sun to be at S, and the 
earth at 4. 4' is the geocentric place of the sun, and G is 
the heliocentric place of the earth. 

The Sun's Apparent Path. 

It is evident that if the apparent path of the sun lay in 
the equator, it would, during the entire year, rise exactly 
in the east and set in the west, and would always cross the 
meridian at the same altitude. The days would always be 
twelve hours long, for the same reason that a star in the 
equator is always twelve hours above the horizon and twelve 
hours below it. But we know that this is not the case, the 
sun being sometimes north of the equator and sometimes 
south of it, and therefore having a motion in declination. 
To understand this motion, suppose that on March 19th, 
1879, the sun had been observed with a meridian circle and a 
sidereal clock at the moment of transit over the meridian of 
Washington. Its position would have been found to be this; 

Eight Ascension, 23^ 55"^ 23' ; Declination, 0° 30' south. 
Had the observation been repeated on the 20th and fol- 
lowing days, the results would have been: 

March 20, R. Ascen. 23^ 59"^ 2' ; Dec. 0° 6' South, 

21, '' 0^ 2™ 40« ; '' 0° 17' North, 

22, '' 0^ 6"^ 19' ; '' o° 41' North. 

If we lay these positions down on a chart, we shall find 
them to be as in Fig. 30, the centra of the sun being south 



1 



MOTIONS OF THE EAUTR 87 

of the equator in the first two joositions, and north of it in 
the last two. Joining the successive positions by a line, we 
shall have a representation of a small portion of the appa- 
rent path of the sun on the celestial sphere, or of the ecliptic. 
It is clear from the observations and the figure that the 
sun crossed the equator between six and seven o'clock on 
the afternoon of March 20th, and therefore that the equa- 
tor and ecliptic intersect at the point where the sun was at 
that hour. This point is called the vernal equinox, the 
first word indicating the season, while the second expresses 




Fig. 30.— The Sun Crossing the Equator. 

the equality of the nights and days which occurs when the 
sun is on the equator. It will be remembered that this 
equinox is the point from which right ascensions are count- 
ed in the heavens, in the same way that we count longi- 
tudes on the earth from Greenwich or Washiugton. A 
sidereal clock at any place is therefore so set that the hands 
shall read hours minutes seconds at the moment 
when the vernal equinox crosses the meridian of the place. 
Continuing our observations of the. sun's apparent course 
for six months from March 20th till September 23d, we 



88 



ASTHOmMY. 



should find it to be as in Fig. 31. It will be seen that Pig* 

30 corresponds to the right- 
hand end of 31, but is on a 
much larger scale. The sun, 
moving along the great circle 
of the ecliptic, will reach its 
greatest northern declination 
about June 21st. This point 
is indicated on the figure as 
90° fi'om the vernal equinox, 
and is called the stimmer sol- 
stice. The sun's right ascen- 
sion is then six hours, and its 
declination 23^° north. The 
student should complete the 
figure by drawing the half not 
given here. 

Tlie course of the sun now 
inclines toward the south, and 
it again crosses the equator 
about September 22d at a point 
diametrically opposite the ver- 
nal equinox. All great circles 
intersect each other in two op- 
posite points, and the ecliptic 
and equator intersect at the two 
opposite equinoxes. The equi- 
nox which the sun crosses on 
September 22d is called the 
autumnal equinox. 

During the six months from 
September to March the sun's 




Motions of the earTS. g9 

Course is a counterpart of that from Marcli to Septem- 
ber, except that it lies south of the equator. It attains 
its greatest south declination about December 22d, in 
right ascension 18 hours and south declination 23° 30'. 
This point is called, the icinter solstice. It then begins to 
incline its course toward the north, reaching the vernal 
equinox again on March 20th, 1880. 

The two equinoxes and the two solstices may be re- 
garded as the four cardinal points of the sun's apparent 
annual circuit around the heavens. Its passage through 
these points is determined by measuring its altitude or de- 
clination from day to day with a meridian circle. Since in 
our latitude greater altitudes correspond to greater declina- 
tions, it follows that the summer solstice occurs on the day 
when the altitude of the sun is greatest, and the winter 
solstice on that when it is least. The mean of these alti- 
tudes is that of the equator, and may therefore be found 
by subtracting the latitude of the place from 90°. The 
time when the sun reaches this altitude going north, marks 
the vernal equinox, and that when it reaches it going south 
marks the autumnal equinox. 

These passages of the sun through the cardinal points have been 
the subjects of astronomical observation from the earliest ages on 
account of their relations to the change of the seasons. An ingeni- 
ous method of finding the time when the sun reached the equinoxes 
was used by the astronomers of Alexandria about the beginning of 
our era. In tlie great Alexandrian Museum, a large ring or wheel 
was set up parallel to the plane of the equator; in other words, it 
was so fixed that a star at the pole would shine perpendicularly on 
the wheel. Evidently its plane if extended must have passed through 
the east and west points of the horizon, while its inclination to the 
vertical was equal to the latitude of the place, which was not far 
from 30°. When the sun reached the equator going north or south, 
and shone upon this wheel, its lower edge would be exactly covered 
by the shadow of the upper edge; whereas in any other position the 



^0 AM'lwMMr. 

sun would shine upon the lower inner edge. Thus the time at which 
tlie sun reached the equinox could be determined, at least to a frac- 
tion of a day. By the more exact methods of modern limes it can 
be determined within less than a minute. 

It will be seen that this method of determiuiug the annual appar- 
ent course of the sun by its declination or altitude is entirely inde- 
pendent of its relation to the fixed stars; and it could be equally well 
applied if ho stars were ever visible. There are, therefore, two en- 
tirely distinct ways of finding when the sun or the earth has completed 
its apparent circuit around the celestial sphere; the one by the transit 
instrument and sidereal clock, which show when the sun returns to 
the same position among the stars, the other by the measurement of 
altitude, which shows when it returns to the sa77ie equino.v. By the 
former method, already described, we conclude that it has completed 
an annual circuit when it returns to the same star; by the latter when 
it returns to the same equinox. These two methods will give slightly 
different results for the length of the year, for a reason to be here- 
after described. 

The Zodiac and its Divisions, — The zodiac is a belt in the heavens, 
commonly considered as extending some 8^ on each side of the 
ecliptic, and therefore about 16° wide. The planets known to the 
ancients are always seen within this belt. At a very early day the 
zodiac was mapped out into twelve signs known as the signs of the 
zodiac, the names of which have been handed down to the present 
time. Each of these signs was supposed to be the seat of a constella- 
tion after which it was called. Commencing at the vernal equinox, 
the first thirty degrees through which the sun passed, or the region 
among the stars in which it was found during the month following, 
was called the sign Aries. The next thirty degrees was called 
Taurus. The names of all the twelve signs in their proper order, 
with the approximate time of the sun's entering upon each, are as 
follows: 

Aries, the Ram, March 20. 

Taurus, the Bull, April 20. 

Gemini, the Twins, May 20. 

Cancer, the Crab, June 21. 

Leo, the Lion, July 22. 

Virgo, the Virgin, August 22. 

Libra, the Bi^lance, September 22. 

Scorpins, the Scorpion, October 23. 

Sagittarius, the Archer, November 23. 

Capricornus, the Goat, December 21. 

Aquarius, the Water-ber.ier, January 20. 

Pisces, the Fishes, February 19. 



MOTiOM OF mM EAttm. 91 

Eafcli of these signs coincides roughly with a constellation in the 
heavens; and thus there are twelve constellations called by the 
names of these signs, but the signs and the constellations no longer 
correspond. Although the sun now crossies the equator and enters 
the sign Aries on the 20th of March, he does not reach the constella- 
iion Aries until nearly a month later. This arises from the preces- 
sion of the equinoxes, to be explained hereafter. 

Obliquity of the Ecliptic. 

We have already stated that when the sun is at the sum- 
iner solstice it is about 23|° north of the equator, and when 
at the winter solstice^ about 23^° south. This shows that 
the ecliptic and equator make an angle of about 23^° with 
each other. This angle is called the obliquity of the eclip- 
tic, and its determination is very simple. It is only neces- 
sary to find by repeated observation the sun's greatest north 
declination at the summer solstice, and its greatest south 
declination at the winter solstice. Either of these declina- 
tions, which must be equal if the observations are accurate- 
ly made, will give the obliquity of the ecliptic. It has been 
continually diminishing from the earliest ages at a rate of 
about half a second a year, or, more exactly, about 47" in 
a century. This diminution is due to the gravitating 
forces of the pl^ets, and will continue for several thousand 
years to come. It will not, however, go on indefinitely, 
but the obliquity will only oscillate between comparatively 
narrow limits. 

In the preceding paragraphs we have explained the 
apparent annual circuit of the sun relative to the equator, 
and shown how the seasons depend upon this circuit. In 
order that the student may clearly grasp the entire subject, 
it is necessary to show the relation oj: these apparent move- 
ments to the actual movement of the earth around the 
§un. 



92 AsmomMT. 

To understand the relation of the equator to the ecliptic, we must 
remember that the celestial pole and the celestial equator have really 
no reference whatever to the heavens, but depend solely on the direc- 
tion of the earth's axis of rotation. The pole of the heavens is noth- 
ing more than that point of the celestial sphere toward which the 
earth's axis happens to point. If the direction of this axis changes, the 
position of the celestial pole among the stars will change also; though 
to an observer on the earth, unconscious of the change, it would 
seem as if the starry sphere moved while the pole remained at rest. 
Again, the celestial equator being merely the great circle in which 
the plane of the earth's equator, extended out to infinity in every 
direction, cuts the celestial sphere, any change in the direction of the 
pole of the earth would necessarily change the position of ihe equator 
among the stars. Now the positions of the celestial pole and the 
celestial equator among the stars seem to remain unchanged through- 
out the year. (There is, indeed, a minute change, but it does not 
affect our present reasoning.) This shows that, as the earth revolves 
around the sun, its nxis is constantly directed toward nearly the 
same point of the celestial sphere. 



The Seasons. 

The conclusions to which we are thus led respecting the 
real revolution of the earth are shown in Fig. 32. Here S 
represents the sun, with the orbit of the earth surrounding it, 
but viewed nearly edgeways so as to be much foreshortened. 
A B CD are tlie four cardinal positions of the earth which 
correspond to the cardinal points of the apparent path of the 
sun already described. In each figure of the earth N8\^ 
the axis, N being its north and 8 its south pole. Since 
this axis points in the same direction relative to the stars 
during an entire year, it follows that the different lines 
N S are all parallel. Again, since the equator does not 
coincide with the ecliptic, these lines are not perpendicular 
to the ecliptic, but are inclined from this perpendicular by 

23^. 

When the earth is at A the sun's north-polar distance (the 



MOTIONS OF THE EARTH. 



93 



angle at the centre of the earth at A between the lines to 
the north pole and to the sun) is 113^°; at B it is 90°; at 
C it is 66|°; at D it is again 90°, and between Q^^ and 
113^° the north-polar distance continually varies. This 
may be plainer if the student draws the lines S A, SB, 
SG, SD, and prolongs the lines N8 at each position of 
the earth. 

IS'ow the sun shines on only one half of the earth; viz., 
that hemisphere turned toward him. This hemisphere is 
left bright in each of the figures of the earth 'dtA,B, O, D, 




Fig. 32.— Causes of the Seasons. 

Consider the diagram at A, and remember that the earth 
is turning round so that every observer is carried round 
his parallel of latitude every 24 hours. The parallels are 
drawn in the cut, and it is plain that a person near iVwill 
remain in darkness all the 24 hours ; any one in the north- 
ern hemisphere is less than half the time in the light — that 
is, the sun is less than half the time above his horizon — 
and a person in the southern hemisphere is more than half 
the time in the light. At the equator the days and nights 



94 



ASTROmUT. 



are always equal. At the south pole it is perpetual day. 
The spectator near the south pole is carried jound in a 
parallel of latitude which is perpetually shined upon. 
This is the ivinter solstice (midwinter in the northern 
hemisphere, midsummer in the southern). 

Next suppose the earth at ^ : ^ is 90° from A ; that is, 
3 months later. The sun's rays just graze the north and 
south poles; each parallel of latitude is half light and half 
dark ; the days and nights are equal. This is the equinox 
of spring — the vernal equinox. The sun's north-polar dis- 
tance is 90°. At C we have the summer solstice (summer 
in the northern hemisphere, winter in tlie soutliern). 
Here is perpetual day at the north pole, perpetual night at 
the south; long days to all the northern hemisphere, long 
nights in the southern. Three months later we have the 
autumnal equinox iit D. 

This change of the seasons depends upon the change of 
the sun's north-polar distance. 

The exact plienomena at each place may be studied b}^ 
constructing a diag]'am for the latitude of that place (see 
page 42) and assuming the sun's north-polar distance as 
follows : , •-, . - „ _ 



March 21, KRD. 90°, 

June 20, N.P.D. QQ>^, 

September 21, N.P.D. 90, 

December 21, N.P.D. 113 J, 



Vernal Equinox. 
Summer Solstice. 
Autumnal Equinox. 
Winter Solstice. 



Two such diagrams are given in the text-book (page 28). 
The student should be able to pro^^e that the sun is always 
in the zenith of some place in the torrid zone. 



MOTIONS OF THE EARTH, 95 



Celestial Latitude and Longitude. 

To describe the positions of the sun and planets in space 
we need two new co-ordinates. 

The Celestial Latitude of a star is its angular distance 
north or south of the ecliptic. 

The Celestial Longitude of a star is its angular distance 
from the vernal equinox measured on the ecli])tic from 
west to east. Having the right ascension and declination 
of a body (which can be liad by observation), we can com- 
pute its celestial latitude and longitude. These co-ordinates 
are no longer observed (as they were by the ancients), but 
deduced from observations of right ascension and declina- 
tion. 



CHAPTER V. 
THE PLANETARY MOTIONS. 

Apparent and Real Motions of the Planets. 

Definitions. — The solar system comprises a number of 
bodies of various orders of magnitude and distance, sub- 
jected to many complex motions. Our attention will be 
particularly directed to the motions of the great planets. 
These bodies may, with respect to their apparent motions, 
be divided into three classes. 

Speaking, for the present, of the sun as a planet, the 
first class comprises the sun and moon. "We have seen that 
if, upon a star chart, we mark down the positions of the 
sun day by day, they will all fall into a regular circle which 
marks out the ecliptic. The monthly course of the moon 
is found to be of the same nature; and although its motion 
is by no means uniform in a month, it is always toward the 
east, and always along or very near a certain great circle. 

The second class comprises Venus and Mercury/. The 
apparent motion of these bodies is an oscillating one on 
each side of the sun. If we watch for the appearance of 
one of these planets after sunset from evening to evening, 
we shall find it to appear above the western horizon. Night 
after night it will be farther and farther from the sun until 
it attains a certain maximum distance; then it will appear 
to return towards the sun again, and for a while to be iQst 



THE PLANETARY MOTIONS. 97 

in its rays. A few days later it will reappear to the west 
of the sun, and thereafter be visible in the eastern horizon 
before sunrise. In the case of Mercurij the time required 
for one complete oscillation back and forth is about four 
months; and in the case of Venus it is more than a year 
and a half. 

The third class comprises Mars, Jupiter, and Saturn, as 
well as a great number of planets not visible to the naked 
eye. The general or average motion of these planets is 
toward the east, a complete revolution in the celestial 
sphere being performed in times ranging from two years in 
the case of Mars to 164 years in that of Neptune. But, 
instead of moving uniformly forward, they seem to have a 
swinging motion; first, they move forward or toward the 
east through a pretty long arc, then backward or westward 
through a short one, then forward through a longer one, 
etc. It is by the excess of the longer arcs over the shorter 
ones that the circuit of the heavens is made. 

The general motion of the sun, moon, and planets among 
the stars being toward the east, motion in this direction is 
called direct; motions toward the west are called retrograde. 
During the periods between direct and retrograde motion 
the planets will for a short time appear stationary. 

The planets Venus and Mercury are said to be at greatest 
elongation when at their greatest angular distance from the 
sun. The elongation which occurs with the planet east of 
the sun, and therefore visible in the western horizon after 
sunset, is called the eastern elongation, the other the west- 
ern one. 

A planet is said to be in conjunction with the sun when 
it is in the same direction as seen from the earth, or when, 
as it seems to pass by the sun^ it approaches nearest to it, 



98 ASTRONOMY. 

It is said to be in opposition to the sun when exactly in the 
opposite direction — rising when the sun sets, and vice 
ver^sa.* If, when a planet is in conjunction, it is between 
the earth and the sun, the conjunction is said to be an 
inferior one; if beyond the sun, it is said to be superior. 




Fig. 33.— Orbits of the Planets. 

Arrangements and Motions of the Planets. — The sun is 
the real centre of the solar system, and the planets proper 
revolve around it as the centre of motion. The order of 
the five innermost large planets, or the relative position of 

* A plauet is in coujunetion with the sun when it has the same 
geocentric longitude; in opposition wli^O the longitudes differ 180°. 



THE PLANETARY MOTIONS. 9^ 

their orbits, is shown in Fig. 33. These orbits are all 
nearly, but not exactly, in the same plane. The planets 
Mercury and Venus which, as seen from the earth, never 
appear to recede very far from the sun, are in reality those 
which revolve inside the orbit of the earth. The planets 
of the third class, which perform their circuits at all dis- 
tances from the sun, are what we call the superior planets, 
and are more distant from the sun than the earth is. Of 
these the orbits of Mars, Jiq^iter, and a swarm of telescopic 
planets are shown in the figure; next outside of Jtqnter 
comes Saturn, the farthest planet readily visible to the 
naked eye, and then Uratius and Neptune, telescopic plan- 
ets. On the scale of Fig. 33 the orbit of Neptune would 
be more than two feet in diameter. Finally, the moon is 
a small planet revolving around the earth as its centre, and 
carried with the latter as it moves around the sun. 

Inferior planets are those whose orbits lie inside that of 
the earth, as Mercury and Venus. 

Superior planets are those whose orbits lie outside that 
of the earth, as Mars, Jupiter, Saturn, etc. 

The farther a planet is situated from the sun the slower 
is its orbital motion. Therefore, as we go from the sun, 
the periods of revolution are longer, for the double reason 
that the planet has a larger orbit to describe and moves 
more slowly in its orbit. It is to this slower motion of the 
outer planets that the occasional apparent retrograde mo- 
tion of the planets is due, as may be seen by studying Fig. 
3i. The apparent position of a planet, as seen from the 
earth, is determined by the line joining the earth and 
planet. Supposing this line to be continued so as to inter- 
sect the celestial sphere, the apparent motion of the planet 
will be defined by the motion of the point in which the line 



100 



ASTRONOMY. 



intersects the sphere. If this motion is toward the east, it 
is direct ; if toward the west, retrograde. 

The Apparent Motion of a Superior Planet. — In the figure 
let S be the sun, ABODE F the orbit of the earth, and 
HIKLMN the orbit of a superior planet, as Mars. 
When the earth is at A suppose Mars to be at H, and let 
B and /, C and K, D and Z, ^ and M, i^ and ^ be corre- 
sponding positions. As the earth moves faster than Mars 




Fig. 34. 

the arcs AB, BC, etc., correspond to greater angles at the 
centre than HI, IK, etc. 

When the earth is at A, Mars will be seen on the celestial 
sphere at the apparent position 0. When the earth is at 
B, Mars will be seen at P. As the earth describes AB, 
Mars will appear to describe OP moving in the same direc- 
tion as the earth's orbital motion; i.e., direct. When the 
earth is at O, Mars is at K (in opposition to the sun), and 
its motion is retrograde along the small arc beyond QP iu 



THE PLANETARY MOTIONS. 101 

the figure. When the earth reaches D the planet has fin- 
ished its retrograde arc. As the earth moves from D to E 
the planet moves from L to M, and the lines joining earth 
and planet are parallel and correspond to a fixed position 
on the celestial sphere. The planet is at a station. As the 
earth moves from E to F the apparent motion of Mars is 
direct from Q to R-, and in the same way the apparent 
motion of any outer planet can be determined by drawing 
its orbit outside of the earth's orbit ABCDEF and laying 
off on this orbit positions which correspond to the points 
ABCBEF and joining the corresponding positions. It 
will be found that all outer planets have a retrograde mo- 
tion at opposition, etc. 

The Apparent Motion of an Inferior Planet. — To deter- 
mine the corresponding phenomena for an inferior planet 
the same figure maybe used. Suppose H I K L M to be 
the orbit of the earth, and A B CD E Fthe orbit of Mer- 
cury, and suppose ^ and A, /and B, etc., to be corre- 
sponding positions. Suppose HA to be tangent to Mer- 
cury's orbit. The angle A H S is the elongation of Mer- 
cury, nnd it is the greatest elongation it can ever have. 

Let the student construct the apparent positions of Mer- 
cury as seen from the earth from the data given in the 
figure. From the apparent positions he can determine the 
apparent motions. As Mercury moves from A B its ap- 
parent motion is direct. On both sides of the inferior con- 
junction C its motion is retrograde. From D to E it is 
stationary. Also let him construct the apparent positions 
of the sun at different times by drawing the lines H S, IS, 
K S, etc., towards the right. The angles between the ap- 
parent positions of Mercury and the sun will be the elonga- 
tions of Mercury at various times. 



102 



ASTRONOMY. 



Theory of Epicycles. — Complicated as the apparent motions of the 
planets were, it was seen by the ancient astronomers that they could 
be represented by a combination of two motions. First, a small circle 
or epicycle was supposed to move around the earth (not the sun) 
with a regular, though not uniform, forward motion, and then the 
planet was supposed to move around the circumference of this circle. 
The relation of this theory to the true one was this: The regular 
forward motion of the epicycle represents the real motion of the 
planet around the sun, while the motion of the planet around the 
circumference of the epicycle is an apparent one arising from the 

revolution of the earth around the 
sun. To explain this we must under- 
stand some of the laws of relative mo- 
tion. 

It is familiarly known that if an 
observer in unconscious motion looks 
upon an object at rest, the object will 
appear to him to move in a direction 
opposite that in which he moves. As 
a result of this law, if the observer is 
unconsciously describing a circle, an 
object at rest will appear to him to 
describe a circle of equal size. This 
is shown by the following figure. Let 
.8 represent the sun, and A B CD E:P 
the orbit of the earth. Let us sup- 
pose the observer on the earth carried 
around in this orbit, but imagining 
himself at rest at 8, the centre of mo- 
tion. Suppose he keeps observing the 
direction and distance of the planet P, 
which for the present we suppose to 
be at rest, since it is only the relative 
Pj(. 35 motion that we shall have to consider. 

When the observer is at A he really 
sees the planet in a direction and distance A P, but imagining himself 
at 8 he thinks he see the planet at the point a determined by drawing 
a line 8a parallel and equal to A P. As he passes from ^ to ^ the 
planet will seem to him to move in the opposite direction from a to 
b, the point b being determined by drawing 8 b equal and parallel 
to BP. As he recedes from the planet through the arc B CD, the 
planet seems to recede from him through bed; and while he moves 
from left to right through DE the planet seems to move from right 




PLA^ETAitt MOTIONS. 103 

to left through de. Final]5^ as he approaches the plauet through 
the arc efa the planet seems to approach him through E F A, and 
■when he returns to A the planet will appear at A, as in the begin. 
Ding. Thus the planet, though really at rest, would seem to him to 
move over the circle ahcdef corresponding to that in which the 
observer himself was carried around the sun. 

The planet being really in motion, it is evident that the combined 
effect of the real motion of the planet and the apparent motion 
around the circle ahcdef viiW be represented by carrying the centre 
of this circle P along the true orbit of the planet. The motion of 
the earth being more rapid than that of an outer planet, it follows 
that the apparent motion of the planet through a & is more rapid 
than the real motion of P along the orbit. Hence in this part of the 
orbit the movement of the planet will be retrograde. In every other 
part it will be direct, because the progressive motion of P will at 
least overcome, sometimes be added to, the apparent motion around 
the circle. 

In the ancient astronomy the apparent small circle abcdefw^ts 
called the epicycle. 

In the case of the inner planets Mercury and Venus the relation of 
the epicycle to the true orbit is reversed. Here the epicyclic motion 
is that of the planet round its real orbit ; that is, the true orbit of the 
planet around the sun was itself taken for the epicycle, while the 
forward motion was really due to the apparent revolution of the sun 
produced by the annual motion of the earth. 

By constructing a figure for this case the student can readily see 
bow this comes about. 

Although the observations of two thousand years ago 
could be tolerably well explained by these epicycles, yet 
with every increase of accuracy in observation new compli- 
cations had to be introduced, until at the time of Copee- 
N"icus (1542) the confusion was very great. 

The Copernican System of the World. — Coperkicus re- 
vived a belief taught by some of the ancients that the sun 
was the centre of the system, and that the earth and plan- 
ets moved about him in circular orbits. While this was a 
step, and a great step, forward, purely circular orbits for 
the planets would not explain all the facts. 



104 A8TR0N0MT. 

From the time of Copernicus (1542) till that of Kep- 
ler and Galileo (1600 to 1630) the whole question of the 
true system of the universe was in debate. The circular 
orbits introduced by Copern^icus also required a complex 
system of epicycles to account for some of the observed 
motions of the planets, and with every increase in accuracy 
of observation new devices had to be introduced into tht 
system to account for the new phenomena observed. In 
short, the system of Copernicus accounted for so many 
facts (as the stations and retrogradations of the planets) 
that it could not be rejected, and had so many difficulties 
that without modification it could not be accepted. 

Kepler's Laws of Planetary Motion. 

Kepler and Galileo. — Kepler (born 1571, d. 1630) was 
a genius of the first order. He had a thorough acquaint- 
ance with the old systems of astronomy and a thorough be- 
lief in the essential accuracy of the Copernican system, 
whose fundamental theorem was that the sun and not the 
earth was the centre of our system. He lived at the same 
time with Galileo, who was the first person to observe the 
heavenly bodies with a telescope of his own invention, and 
he had the benefit of accurate observations of the planets 
made by Tycho Brake. The opportunity for determin- 
ing the true laws of the motions of the planets existed then 
as it never had before; and fortunately he was able, 
through labors of which it is difficult to form an idea to- 
day, to reach a true solution. 

The Periodic Time of a Planet.— The time of revolution 
of a planet in its orbit round the sun (its periodic time) 
can be learned by continuous observations of the planet's 
course among the stars. 



THM PLANETARY MOTIONS. io5 

From ancient times the geocentric positions of the 
planets had been observed. These positions were referred 
to the places of the brightest fixed stars, and the relative 
places of these stars had been fixed with a tolerable ac- 
curacy. The time required for a planet to move from one 
star to the same star again was the time of revolution of 
the planet referred to the earth. 

The real motion of the earth was known from observa- 
tions of the apparent motion of the sun. By calculation 
it was possible to refer the motions as ohserved (i.e., with 
reference to the earth) to the real motions (i.e., those about 
the sun). 

It was thus found that the periodic times of the known 
planets were: 



For Mercury 


about 88 


Venus 


225 


Earth 


B65 


Mars 


687 


Jupiter 


" 4333 


Saturn 


" 10,759 



These values were known to the predecessors of Copek- 
Ficus. He also showed (what is evident when we examine 
Fig. 34) that to an observer on the sun the motions of 
the planets would be always direct, and that no stations or 
retrogradations of the planets would be seen from the sun. 

In Fig. 36 let Sho, the sun, E the earth, and Ma planet. 
Suppose the lines 8E and S M drawn. They will meet 
the celestial sphere at points whose positions with refer- 
ence to the fixed stars could be ascertained by obser- 
vation. The relative positions of these fixed stars were 
also known by previous observations. The angle E' 8 E" 
was thus known since it was determined by the angular 



106 



ASTRONOMY. 



distance of the stars supposed to be at E' and E''. The 
angle M E S was known, since it could be directly measured 
(the elongation of M from the sun). Hence the other angle 
of the triangle MSB was known, since it was 180° less the 
sum of E'8 E" and SEM. Therefore a triangle could be 
constructed ^ivliich should have the same shape as if ^^S. 
In such a triangle S3I would represent the distance of the 




Fig. 36. 

planet from the sun, and SE the distance of the earth. 

The ratio -^^ could then be determined. Nothing was 

known, from this calculation, of the absolute value ofSE 
or /S if in miles, but observations of this sort on all the 
planets gave the value of their distances from the sun in 
terms of the distance of the earth from the sun. It is 
often convenient to call the distance >S'^ unity; and if SE 
be taken as the astrono^nical unit, it has been found that 



THE PLANETARY MOTIONS. 107 



Mercury a^ 


= 0.3871 


Venus a-i 


= 0.7233 


Earth aa 


= 1.0000 


Mars a 4 


= 1.5237 


Jupiter as 


= 5.2038 


Saturn a^ 


= 9.5388 



The calculation which we have described could be made 
for every position of each planet, and thus its distances from 
the sun at every point of its orbit could be determined. 

The radius-vector of a planet is the line ivhich joins it to 
the sun. 

The relative lengths of the radii-vectores of each planet 
at any time were thus found by observation, in terms of 
the earth's radius-vector = 1. 




Suppose jS^to be the sun, and draw lines SP, SP^, S P^, 
S P^f etc., to the heliocentric positions of a planet at dif- 
ferent times. On these lines lay off distances SP, SP^, 
SP,, etc., proportional to the lengths of the planet's radii- 
vectores determined as above. Join the points P, P^, P,, 
Pj, etc. The line joining these is a visible representation 



108 



ASTRONOMY. 



of the shape of the planet's orbit, drawn to scale. This 
shape is not that of a circle, but it is an ellipse, and the 
sun, 8, is not at the centre but at a focus of the ellipse. 

All ellipse is a curve such that the sum of the distances 
of every point of the curve from tivo fixed points (the foci) 
is a constant quantity. 




Fig 88. 

The Ellipse.—^ D C P is an ellipse ; S and *S' are the foci. By the 
definition of an e\\'\psQ SP-\- P S'= AG, and this is true for every 
point. S is the focus occupied by the sun, " the filled focus." A S 
is the least distance of the planet from the sun, its perihelion distance; 
and A is the perihelion, that point nearest the sun. C is the aphelion, 
the point farthest from the sun. 8 A, SD, SO, SB, 8P are radii- 
vectores at different parts of the orbit. AG\s, the major axis 
of the orbit = 2a. This major axis of the orbit is twice the mean 
distance of the planet from the sun. a. BD\s the minor axis, 2b. 
The ratio of S io OA is the eccentricity of the ellipse. By the 
definition of the ellipse, again, BS-^BS'= A C ; and 2?-S = BS— a. 



ellipse is 



BO -\-0S^,o\' OS- Va"^-})^ and the eccentricity of the 

OS _ V'^-h'^ 
0A~ a ' 



Kepler's Laws. — By computations based on the observa- 
tions of Mars made by Tycho Brake, Kepler deduced 



THE PLANETARY MOTIONS. 109 

his first two laws of motion in the solar system. The first 
law of Kepler is — 

/. Each planet moves around the sun in an ellipse, hav- 
ing the sun at one of its foci. To understand Law II: 

Suppose the planet to be at the points F, P^, P„ P„ P^, 
etc., at the times T, T^, T,, T^, T^, etc. (Fig. 37). 

Suppose the times T- T, 1\- T^, T^- T^ to be equal. 
Kepler computed the areas of the surfaces P SP^, P^S P^, 
P^ /S'Pj and found that these areas were equal also, and 
that this was true for each planet. The second law of Kep- 
ler is — 

//. 77ie radius-vector of each planet describes equal areas 
in equal times. 

These two laws are true for each planet moving in its 
own ellipse about the sun. 

For a long time Kepler sought for some law which 
should connect the motion of one planet in its ellipse with 
the motion of another planet in its ellipse. Finally he 
found such a relation between the mean distances of the 
diiferent planets (see table on page 107) and their periodic 
times (see table on p. 105). 

His third law is: 

///. The squares of the periodic tiines of the planets are 
proportional to the cubes of their mean distances from the 
sun. 

That is, if T^, T^, T^, etc., are the periodic times of the 
different planets whose mean distances are a^, «,, a^, etc., 
then 



/7T2 . mi 


z=z 


^/ :<; 


nil , rp -x 


= 


< : «,'; 


etc. 




etc. 



110 ASTMomMT. 

If 5^3 and a^ are the periodic time and the mean distance 
of the earth, and if T', (= 1 year) is taken as the unit of 
time and a^ as the unit of distance, then we shall have 

T' :1 = a' : 1 or ^ = 1 or ^ = 1: 

T,' :1 = «/ : 1 or ^ = 1 or -^ = 1; 

and so on. 

The data which Kepler had were not quite so accurate 
as those which we have given, and the table below shows 
the very figures on which Kepler's conclusion was based: 

Planet. «§ T T ^ a^ 

Mercury 0.2378 . 2408 years 1.013 

Venus 0.6104 0.6151 1.008 

Earth. 1.0000 1.0000 1.000 

Mars 1.8740 1.8810 1.004 

Jxipiter 11.914 11.8764 0.996 

Saturn 28.058 29.4605 1.050 

Although the numbers in the third column were not 
strictly the same, their differences were no greater than 
might easily have been produced by the errors of the obser- 
vations which Kepler used; and on the evidence here 
given he advanced his third law. The order of discovery 
of the true theory of the solar system was, then — 
I. To prove that the earth moved in space; 
II. To prove that the centre of this motion was the sun; 

III. To establish the three laws of Kepler, which gave 
the circumstances of this motion. 

By means of the first two laws of Keplek the motions of each 
planet in its own ellipse became known; that is, the position of the 
planet at any future time could be predicted. For example, if the 
planet was at P at a time 7, and the question was as to its place at a 
subsequent time T, this could be solved by computing, first, how 



Tim PLANETARY MOTIONS. HI; 

large an area would be described by the radius-vector in the interval 
T" — 7'/ and second, what the angle at S of the sector having this 
area would be. Then drawing a line through S making this angle 
with the line )SP(say SP), and laying ofT the length of the radius- 
vector SP^, the position of the planet became known. 

From the third law the relative values of the mean distances 
«i, ai, di, as, etc., could be determined with great and increasing ac- 
curacy. 

T 
From the equation— = 1, a could be determined so soon as T was 

known. AVith each revolution of the planet jT became known more 
accurately, as did also a. 

These laws are the foundations of our present theory of the solar 
system. They were based on observation pure and simple. We may 
anticipate a little to say that these laws have been compared with 
the most precise observations we can make at the present time, and 
discussed in all their consequences by processes unknown to Kep- 
ler, and that they are strictly true if we make the following modifi- 
cations. 

If there were only one planet revolving about the sun, then it 
would revolve in a perfect ellipse, and obey the second law exactly. 
In a system composed of the sun and more than one planet each 
planet disturbs the motion of every other slightly, by attracting it 
from the orbit which it would otherwise follow. 

Thus neither the first nor the second law can be precisely true of 
any planet, although they are very nearly so. In the same way the 
relation between the orbits of any two planets as expressed in the 
third law is not prrcise, all hough it is a very close approximation. 

Elements of a Planet's Orbit. — When we know a auci b for any orbit, 
the shape and size of the orbit is known. 

Knowing a we also know T, the periodic time; in fact a is found 
from 7 by Kepler's law III. 

If we know the planet's celestial longitude (L) at a given epoch, 
say December 31st. 1850, we have all the elements necessary for 
finding the place of the planet in its orbit at any time, as has been 
explained (page 110). 

The orbit lies in a certain plane; this plane intersects the plane of 
the ecliptic at a certain angle, which we call the inclination i. Know- 
ing i, the plane of the planet's orbit is fixed. The plane of the 
orbit intersects the plane of the ecliptic in a line, the line of the nodes. 
Half of the planet's orbit lies below (south of) the plane of the 
ecliptic and half above. As the planet moves in its orbit it must 
pass through the plane of the ecliptic twice for every revolution. 



112 ASTRONOMY. 

The point where it passes through the ecliptic going from the south 
lialf to the north half of its orbit is the ascending node; the point 
where it passes througli the ecliptic going from norlii to south is 
the descending node of the planet's orbit. If we have only the in- 
clination given, the orbit of tiie planet may lie anywhere in the plane 
whose angle with the ecliptic is i. If we fix tiie place of the nodes, 
or of one of them, the orbit is thus fixed in its plane. This we do 
by giving the (celestial) longitude of the ascending node/2. 

Now everything is known except the relation of the planet's orbit 
to the sun. This is fixed by the longitude of the perihelion, or P. 

Thus the elements of a planet's orbit are: 

i, the inclination to the ecliptic, which fixes the plane of the planet's 
orbit; 

jQ, the longitude of the node, which fixes the position of the line of 
Intersection of tiie orbit and the ecliptic; 

P, the longitude of the perihelion, which fixes the position of the 
major axis of the planet's orbit with relation to the sun, and hence 
in space; 

a and e, the mean distance and eccentricity of the orbit, which fix 
the shape and size of the orbit; 

2 and M, the periodic time and the longitude at epoch, which enable 
the place of the planet in its orbit, and hence in space, to be fixed at 
any future or past time. 

The elements of the older planets of the solar system are now 
known with great accuracy, and their positions for two or three cen- 
turies past or future can be predicted with a close approximation to the 
accuracy with which these positions can be observed. 



CHAPTER VI. 
UNIVERSAL GRAVITATION. 

Newton's Laws of Motion 

The csiablisbment of the theory of universal gravitation 
furnishes one of the best examples of scientific method 
which is to be found. We shall describe its leading features, 
less for the purpose of making known to the reader the 
technical nature of the process than for illustrating the 
true theory of scientific investigation, and showing that such 
investigation has for its object the discovery of what we 
may call generalized facts. The real test of progress is 
found in our constantly increased ability to foresee either 
the coui-se of nature or the effects of any accidental or arti- 
ficial combination of causes. So long as prediction is not 
possible, the desires of the investigator remain unsatisfied. 
When certainty of prediction is once attained, and the 
Jaws on which the prediction is founded are stated in their 
simplest form, the work of science is complete. 

To the pre-Newtonian astronomers the phenomena of 
the geometrical laws of planetary motion, which we have 
just described, formed a group of facts having no connection 
with anything on the earth's surface. The epicycles of 
HiPPARCHUS and Ptolemy were a truly scientific concep- 
tion, in that they explained the seemingly erratic motions 
of the planets by a single simple laWf In the heliocentric 



114 ASTRONOMY. 

theory of Coperi^-icus this law was still further simplified 
by dispensing in great part with the epicycle, and replacing 
the latter by a motion of the earth around the sun, of the 
same nature with the motions of the planets. But Coper- 
nicus had no way of accounting for, or even of describing 
with rigorous accuracy, the small deviations in the motions 
of the planets around the sun. In this respect he made no 
real advance upon the ideas of the ancients. 

Kepler, in his discoveries, made a great advance in rep- 
resenting the motions of all the planets by a single set of 
simple and easily understood geometrical laws. Had the 
planets followed his laws exactly, the theory of planetary 
motion would have been substantially complete. Still, 
further progress was desired for two reasons. In the first 
place, the laws of Kepler did not perfectly represent all 
the planetary motions. When observations of the greatest 
accuracy were made, it was found that the planets deviated 
by small amounts from the ellipse of Kepler. Some small 
emendations to the motions computed on the elliptic theory 
were therefore necessary. Had this requirement been ful- 
filled, still another step would have been desirable; namely, 
that of connecting the motions of the planets with motions 
upon the earth, and reducing them to the same laws. 

Notwithstanding the great step which Kepler made in 
describing the celestial motions, he unveiled none of the 
great mystery in which they were enshrouded. When Kep- 
ler said that observation showed the law of planetary mo- 
tion to be that around the circumference of an ellipse, as 
asserted in his law, he said all that it seemed possible to 
learn, supposing the statement perfectly exact. And it 
was all that could be learned from the mere study of the 
planetary motions. In order to connect these motions with 



UmVEBSAL GRAVITATION. 115 

those on the earth, the next step was to study the laws of 
force and motion here around us. Singular though it may 
appear, the ideas of the ancients on this subject were far 
more erroneous than their conceptions of the motions of 
the planets. We might almost say that before the time of 
Galileo scarcely a single correct idea of the laws of motion 
was generally entertained by men of learning. Among 
those who, before the time of Newtok, prepared the way 
for the theory in question, Galileo, Huygheks, and 
HooKE are entitled to especial mention. The general laws 
of motion laid down by Newtoi^ were three in number. 

Law First: Every body preserves its state of rest or of 
uniform motion in a right line, unless it is compelled to 
chaiige that state hy forces impressed thereon. 

. It was formerly supposed that a body acted on by no force tended 
to come to rest. Here lay one of tbe greatest difficulties \vbicli the 
predecessors of Newton found, in accounting for tbe motion of tbe 
planets. Tbe idea tbat tbe sun in some way caused tbese motions 
was entertained from tbe earliest times. Even Ptolemy bad a vague 
idea of a force wbicb was always directed toward tbe centre of the 
earth, or, which was to him tbe same thing, toward tbe centre of the 
universe, and which not only caused heavy bodies to fall, but bound 
the whole universe togetlter. Kepler, again, distinctly affirms the 
existence of a gravitating force by which the sun acts on tbe planets; 
but he supposed tbat the sun must also exercise an impulsive forward 
force to keep the planets in motion. The reason of this incorrect 
idea was, of course, tbat all bodies in motion on the surface of the 
earth bad practically come to rest. But what was not clearly seen 
before the time of Newton, or at least before Galileo, was that 
this arose from the inevitable resisting forces which act upon all 
moving bodies upon the earth. 

Law Second: The alteration of motion is ever propor- 
tional to the moving force impressed, and is made iii the 
direction of the right line in wlmlt' tM/ofce mH^ 



116 ASTliONOMT. 

The first law might be considered as a particular case of this sec- 
ond one which arises when the force is supposed to vanish. The ac- 
curacy of both laws can be proved only by very carefully conducted 
experiments. They are now considered as conclusively proved. 

Law Third: To every action there is aliuays opposed an 
equal reaction ; or the mutual actions of two bodies upon 
each other are always equal, and in opposite directions. 

That is, if a body A acts in any way upon a body B, B will exert 
a force exactly equal on A in the opposite direction. 

These laws once established, it became possible to calculate the mo- 
tion of any body or system of bodies when once the forces which act 
on them were known, and, vice versa, to define what forces were re- 
quisite to produce any given motion. The question which presented 
itself to the mind of Newton and his contemporaries was this: Under 
what law of force will planets move round the sun in accordance with 
Kepler's laws f 

Supposing a body to move around in a circle, and putting R the 
radius of the circle, T the period of revolution, HuYGHENshad shown 
that the centrifugal force of the body, or, which is tlie same thing, 
the attractive force toward the centre which would keep it in the 

circle, was proportional to -^. But by Kepler's third law T^ is pro- 
portional to R^. Therefore this centripetal force is proportional to 
-z=-; that is, to -TJX. Thus it followed immediately from Kepler's 

third law that the central force which would keep the planets in their 
orbits was inversely as the square of the distance from the sun, sup- 
posing each orbit to be circular. The first law of motion once com- 
pletely understood, it was evident that the planet needed no force 
impelling it forward to keep up its motion, but that, once started, it 
"w^ould keep on forever. 

The next step was to solve the problem. What law of force will 
make a planet describe an ellipse around the sun, having the latter 
in one of its foci? Or, supposing a planet to move round the sun, 
the latter attracting it with a force inversely as the square of the dis- 
tance; what will be the form of the orbit of the planet if it is not cir- 
cular? A solution of either of these problems was beyond the power 
of mathematicians before the time of Newton; and it thus remained 
uncertain whether the planets moving under the influence of the 
sun's gravit?ition woiild ov would not describe ellipses. Unable, a^ 



UNIVERSAL GRAVITATION. 117 

first, to reach a satisfactory solution, Newton attacked the problem 
in another direction, starting from the gravitation, not of the sun, 
but of the earth, as explained in the following section. 

Gravitation in the Heavens. 

The reader is probably familiar with the story of NeW- 
TOif and the falling apple. Although it has no authorita- 
tive foundation, it is strikingly illustrative of the method 
by which Newton must have reached a solution of the 
problem. The course of reasoning by which he ascended 
from gravitation on the earth to the celestial motions was as 
follows : We see that there is a force acting all over the earth 
by which all bodies are drawn toward its centre. This 
force is called gravitation. It extends without sensible 
diminution to the tops not only of the highest buildings, 
but of the highest mountains. How much higher does it 
extend? Why should it not extend to the moon? If it 
does, the moon would tend to drop toward the earth, just 
as a stone thrown from the hand drops. As the moon 
moves round the earth in her monthly course, there must 
be some force drawing her toward the earth; else, by the 
first law of motion, she would fly entirely away in a straight 
line. Why should not the force which makes the apple 
fall be the same force which keeps her in her orbit? To 
answer this question, it was not only necessary to calculate 
the intensity of the force which would keep the moon her- 
self in her orbit, but to compare it with the intensity of 
gravity at the earth's surface. It had long been known 
that the distance of the moon was about sixty radii of the 
earth, from measures of her parallax (see page 57). If 
this force diminished as the inverse square of the distance, 
then at the mooxi it would be only y^^ as great as at the 



118 ASTRONOMY. 

surface of the earth. On the earth a body falls sixteen feet 
in a second. If, then, the theory of gravitation were cor- 
rect, the moon ought to fall towards the earth g^Vo ^^ ^^^s 
amount, or about ^V ^^ ^.n inch in a second. The moon 
being in motion, if we imagine it moving in a straight line 
at the beginning of any second, it ought to be drawn away 
from that line ^^ of an inch at the end of the second. 
When the calculation was made it was found to agree ex- 
actly with this result of theory. Thus it was shown that 
the force which holds the moon in her orbit is the same 
force that makes the stone fall, diminished as the inverse 
square of the distance from the centre of the earth. 

It thus appeared that central forces, both toward the sun 
and toward the earth, varied inversely as the squares of the 
distances. Kepler's second law showed that the line drawn 
from the planet to the sun would describe equal areas in 
equal times. Newtoi^ showed that this could not be true 
unless the force which held the planet was directed toward 
the sun. We have already stated that the third law showed 
that the force was inversely as the square of the distance, 
and thus agreed exactly with the theory of gravitation. It 
only remained to consider the results of the first law, that 
of the elliptic motion. After long and laborious efforts, 
Newton was enaoled to demonstrate rigorously that this 
law also resulted from the law of the inverse square, and 
could result from no other. Thus all mystery disappeared 
from the celestial motions; and planets were shown to be 
simply heavy bodies moving according to the same laws that 
were acting here around us, only under very different cir- 
cumstances. All three q/" Kepler's laws tvere embraced in 
the single laiv of gravitatian toivard the sun. The sun at- 
tracts the planet§ as tUe eartli attracts bodies Uere ^roi^n(l us. 



VNITERSAL GHAVlTATIOK. 119 

Mutual Action of the Planets. — By Newton's third law of motion, 
each planet must attract the sun with a force equal to that which the 
sun exerts upon the planet. The moon also must attract the earth 
as mucli as the earth attracts the moon. Such being the case, it 
must be highly probable that the planets attract each other. If so, 
Kepler's laws can only be an approximation to the truth. The sun, 
being immensely more massive than any of the planets, overpowers 
their attraction upon each other, and makes the law of elliptic mo- 
tion very nearly true. But still the comparatively small attraction 
of the planets must cause some deviations. Now, deviations from 
the pure elliptic motion were known to exist in the case of several of 
the planets, notably in that of the moon, which, if gravitation were 
universal, must move under the influence of the combined attraction 
of the earth and of tlie sun. Newton, therefore, attacked the com- 
plicated problem of the determination of the motion of the moon 
under the combined action of these two forces. Pie showed in a 
general way that its deviations would be of the same nature as those 
shown by observation. But the complete solution of the problem, 
which required the answer to be expressed in numbers, was beyond 
his power. 

Gravitation Resides in each Particle of Matter. — Still 
another question arose. Were these mutually attractive 
forces resident in the centres of the several bodies attracted, 
or in each particle of the matter composing them? New- 
ton" showed that the latter must be the case, because the 
smallest bodies, as well as the largest, tended to fall toward 
the earth, thus showing an equal gravitation in every sepa- 
rate part. It was also shown by Newton that if a planet 
were on the surface of the earth or outside of it, it would 
be attracted with the same force as if the whole mass 
of the earth were concentrated in its centre. Putting 
together the various results thus arrived at, Newton" 
was al^le to formulate his great law of universal gravita- 
tion in these comprehensive vfidr({^\ " Every particle of 
matter in the universe attracts every other particle ivith 
a force directly as the masses of the two particles, and 



120 ASTRONOMY. 

inversely as the square of the distance which separates 
thern.^' 

To show tlie nature of the attractive forces among these various 
particles, let us represent by m and w' the masses of two attracting 
bodies. We may conceive the body m to be composed of m par- 
ticles, and tlie other body to be composed of m' particles. Let us 
conceive that each particle of one body attracts each particle of the 

other with a force — ,. Then every particle of ui will be attracted by 
each of the m' particles of the other, and therefore the total attractive 
force on each of the m particles will be —^. Each of the m particles 
being equally subject to this attraction, the total attractive force be- 
tween the two bodies will be — —• When a given force acts upon 

a body, it will produce less motion the larger the body is, the accel- 
erating force being proportional to the total attracting force divided 
by the mass of the body moved. Therefore the accelerating force 
which acts on the body m', and which determines the amount of 

1)1 
motion, will be -r^; and conversely the accelerating force acting on 

the body m will be represented by the fraction —^. 



Remarks on the Theory of Gravitation. 

The real nature of the great discovery of Newton is so 
frequently misunderstood that a little attention may be 
given to its elucidation. Gravitation is frequently spoken 
of as if it were a theory of Newton's, and very generally 
received by astronomers, but still liable to be ultimately 
rejected as a great many other theories have been. Not 
infrequently people of greater or less intelligence are found 
making great efforts to prove it erroneous. Newton did 
not discover any new force, but only showed that the 
motions of the heavens could be accounted for by a force 
which we all know to exist. Gravitation (Latin gravitas — 



trmVEBSAL GilAyiTATIOlf. 1^1 

Weight, heaviness) is the force which makes all bodies 
here at the surface of the earth tend to fall downward; 
and if any one wishes to subvert the theory of gravitation, 
he must begin by proving that this force does not exist. 
This no one would think of doing. What Newtois^ did 
was to show that this force, which, before his time, had 
been recognized only as acting on the surface of the earth, 
really extended to the heavens, and that it resided not only 
in the earth itself, but in the heavenly bodies also, and in 
each particle of matter, however situated. To put the 
matter in a terse form, what NEWTOj;r discovered was not 
gravitation, but the universality of gravitation. 

It may be inquired, is the induction which supposes 
gravitation universal so complete as to be entirely beyond 
doubt? We reply that within the solar system it certainly 
is. The laws of motion as established by observation and 
experiment at the surface of the earth must be considered 
as mathematically certain. It is an observed fact that the 
planets in their motions deviate from straight lines in a 
certain way. By the first law of motion, such deviation 
can be produced ouly by a force; and the direction and 
intensity of this force admit of being calculated once that 
the motion is determined. When thus calculated, it is 
found to be exactly represented by one great force con- 
stantly directed toward the sun, and smaller subsidiary 
forces directed toward the several planets. Therefore no 
fact in nature is more firmly established than that of uni- 
versal gravitation, as laid down by Newto^^^, at least within 
the solar system. 

We shall find, in describing double stars, that gravita- 
tion is also found to act between the components of a great 
number of such stars. It is certain, therefore, that at 



12g AsmomMt. 

kast sOmie stars gravitate toward each other, as the bodies 
of the solar system do; but the distance which separates 
most of the stars from each other and from our sun is so 
immense that no evidence of gravitation between individual 
stars and the sun has yet been given by observation. Still, 
that they do gravitate according to Newto:n^'s law can 
hardly be seriously doubted by any one who understands 
the subject. 

The student may now be supposed to see the absurdity 
of supposing that the theory of gravitation can ever be 
subverted. It is not, however, absurd to suppose that it 
may yet be shown to be the result of some more general 
law. Attempts to do this are made from time to time 
by men of a philosophic spirit; but thus far no theory of 
the subject having much probability in its favor has been 
propounded. 



TSl MOTIONS AND ATTRACTION OF THE MOON. 

Each of the planets, except Mercury and Veims, is at- 
tended by one or more satellites, or moons as they are 
sometimes familiarly called. These objects revolve around 
their several planets in nearly circular orbits, accompany- 
ing them in their revolutions around the sun. Their dis- 
tances from their planets are very small compared with the 
distances of the latter from each other and from the sun. 
Their magnitudes also are very small compared with those 
of the planets around which they revolve. Considering 
each system by itself, the satellites revolve around their 
central planets, or '^primaries," in nearly circular orbits, 
and in each system Kepler's laws govern the motion of the 
satellites about the primary. Each system is carried around 
the sun without any derangement of the motion of its sev- 
eral bodies among themselves. 

Our earth has a single satellite accompanying it in this 
way, the moon. It revolves around the earth in a little 
less than a month. The nature, causes, and consequences 
of this motion form the subject of the present chapter. 

The Moon's Motions and Phases. 

That the moon performs a monthly circuit in the heavens is a fact 
with which we are all familiar from childhood. At certain times we 
see her newly emerged from the sun's rays in the western twilight, 
and then we call her the new moon. On each succeeding evening- 



124 ASTRONOMY. 

we see her further to the east, so that in two weeks she is opposite 
the sun, rising in the east as he sets in the west. Continuing her 
course two weeks more, she has approached the sun on tlie other 
side, or from the west, and is once more lost in his rays. At the end 
of twenty- nine or thirty days, we see her again emerging as new 
moon, and her circuit is complete. The sun has been apparently 
moving toward the east among the stars during the whole month, so 
that during the interval from one new moon to the next the moon 
has to make a complete circuit relatively to the stars, and to move 
forward some 30° further to overtake the sun, which has also been 
moving toward the east at the rate of 1° daily. The revolution of 
the moon among the stars is performed in about 27^ days,* so that if 
we observe when the moon is very near some star, we shall find her 
in the same position relative to the star at the end of this interval. 

The motion of the moon in this circuit differs from the apparent 
motions of the planets in being always forward. We have seen that 
the planets, though, on the wiiole, moving toward the east, are 
effected with an apparent retrograde motion at certain intervals, ow- 
ing to the motion of the earth around the sun. But the earth is the 
real centre of the moon's motion, and carries the moon along with it 
in its annual revolution around the sun. To form a correct idea of 
the real motion of these three bodies, we must imagine the earth per. 
forming its circuit around the sun in one year, and carrying with it 
the moon, which makes a revolution around it in 27 days, at a dis- 
tance only about ^i „ that of the sun. 

Phases of the Moon. — The moon, being a non-luminous 
body, shines only by reflecting the light falling on her from 
some other body. The principal source of light is the sun. 
Since the moon is si^herical in shape, the sun can illumi- 
nate one half her surface. The appearance of the moon 
varies according to the amount of her illuminated hemi- 
sphere which is turned toward the earth, as can be seen by 
studying Fig. 39. Here the central globe is the earth; 
the circle around it represents the orbit of the moon. The 
rays of the sun fall on both earth and moon from the 
right, the distance of the sun being, on the scale of the 

* More exactly, 27.32166'i. 



MOTIONS AND ATTRACTION OF THE MOON 125 

figure, some 30 feet. Eight positions of the moon are 
shown around the orbit at A, E, C, etc., and the right- 
hand hemisphere of the moon is illuminated in each posi- 
tion. Outside these eight positions are eight others show- 
ing how the moon looks as seen from the earth in each 
position. 

At A it is "new moon/' the moon being nearly between 




Fig. 



the earth and the sun. Its dark hemisphere is then turn- 
ed toward the earth, so that it is entirely invisible. The 
sun and moon then rise and set together. 

At E the observer on the earth sees about a fourth of 
the illuminated hemisphere, which looks like a crescent, as 
shown in the outside figure. In this position a great deal 
of light is reflected from tlie earth to the moon, rendering 



126 ASmONOMT. 

the dark part of the latter visible by a gray light. This 
appearance is sometimes called the ^^old moon in the new 
moon's arms." At C the moon is said to be in her "first 
quarter," and one half her illuminated hemisphere is visi- 
ble. The moon is on the meridian at 6 p.m. At G three 
fourths of the illuminated hemisphere is visible, and at B 
■the whole of it. The latter position, when the moon is 
opposite the snn, is called "full moon." The moon rises 
at sunset. After this, at H, D, F, the same appearances 
are repeated in the reversed order, the position D being 
called the "last quarter." 

The Tides. 

It Is not possible in. an elementary treatise to give a complete ac- 
count of the theory of the tides of the ocean due to the effect of the 
sun and moon. A general account may be presented wliich will be 
sufficient to show the nature of the effects produced and of their 
causes. 

Let us consider the earth to be composed of a solid centre sur- 
rounded by an ocean of uniform (and not very great) depth. The 
moon exercises an attraction upon every particle of the earth's mass, 
solid and fluid alike. The attraction of the whole moon {M) upon 

a particle m is — ^-, where p is the distance from the centre of the 

moon to m. If ra is one of the solid particles of the earth, it cannot 
move towards M in obedience to the attraction unless all the other 
solid particles move, since the earth proper is rigid. 
If m is a:fluid particle, it is free to move in obedience to the forces 

impressed upon it. The attraction of Jf is proportional to ~^\ that is, 

the particles nearest M are most attracted, and, on the whole, the 
water on the part of the earth nearest the moon will be raised to- 
ward M. 

The moon also attracts the solid parts of the earth more than she 
attracts the water most distant from her, and tliis produces exactly 
the same effect as if there was another moon M exactly opposite to 
M. The elevation of the water under M' will not be quite as great 
as that under M, on account of the increased distance from M. 



MOTIONS AND ATTRACTION OF THE MOON 127 

Thus the moon's action tends to elevate the whole mass of water on 
the line joining her centre with the centre of the earth, and this is so 
not only on the part of this line nearest the moon, but also on that 
farthest from her. 

This elevation of the waters of the ocean above their mean level is 
called the tide. The tidal effect of the moon produces a distortion of 
the spherical shell of water which we have supposed to surround the 
earth, and elongates this shell into the shape of an ellipsoid, the longer 
axis of which is always directed to the moon. Now as the moon 
moves around the eartli once in 24*^ 54"", this ellipsoidal shape must 
also move with her. The crest of the wave directly under M would 
come back to the same meridian every 24'' 54"". The outer crest (under 
M') would come 12'' 27"" after the first, so there would be two liigh 
tides at any one meridian every (lunar) day. The first (and largest) 
high tide would be at the time of the moon's visible transit over the 
meridian. The second high tide would be 12'^ 27'*' later, when the 
moon was on the lower meridian of the place. 

The high tides occur when there is more water than the mean 
depth, and between these high tides we should have low tides, two 
in each lunar day. Similarly there would be two high tides daily at 
each meridian, due to the attractive force of the sun. These would 
have a period of 24 hours and could not always agree with the lunar 
high tides. When the solar and lunar high tides coincided (at new 
and full moon), then we should have the highest high tides and the 
lowest low tides. (These are the Spring tides, so called.) When the 
moon and the sun were 90° apart (moon at first and third quarter), 
then we should have the lowest high tides and tlie highest low tides. 
(Neap tides, so called.) 

The tide-producing force of the moon is to that of the sun as 800 ia 
to 355. The great mass of the sun compensates in some degree foy 
his relatively great distance. 

At spring tides sun and moon work together; at neap tides they 
oppose each other. The relative heights are as 800 -j- 355 : 800 — 355, 
or a,s 13 to 5 approximately. 

The explanation above relates to an earth covered by an ocean of 
uniform depth. To fit it to the facts as they are, a thousand cir- 
cumstances must be taken into account, which depend upon the 
modifying effects of continents and islands, of deep and shallow 
seas, of currents and winds. Practically, the high tide at any sta- 
tion is predicted by adding to the time of the moon's transit over 
its meridian a quantity determiued from observatioft au^ not from 
theory 



128 ASTRONOMY. 

Effects of the Tides upon the Earth's Rotation. — As the tide-wave 
moves it meets with resistauce due to friction. The amount of this 
resistance is subtracted daily from the earth's energy of rotation. 
The tides act on the earth, in a way, as if they were a light friction- 
brpke applied to an enormously heavy wheel turning rapidly. The 
wheel has been set to turning, and, so far as we know, it will never 
have any more rotative energy given to it. Every subtraction of 
energy, however small, is a positive and irretrievable loss. 

The lunar tides are gradually, though very slowly, lengthening the 
day. Since accurate astronomical observations began there has been 
no obserxational proof of any appreciable change in the length of the 
day, but the change has been going on nevertheless. 



CHAPTER VIII. 

ECLIPSES OF THE SUN AND MOON. 

Eclipses are phenomena arising from the shadow of one 
"body being cast upon another, or from a dark body passing 
over a bright one. In an eclipse of the sun, the shadow of 
the moon sweeps oyer the earth, and the sun is wholly or 
partially obscured to observers on that part of the earth 
where the shadow falls. In an eclipse of the moon, the 
latter enters the shadow of the earth, and is wholly or 
partially obscured in consequence of being deprived of 
some or all of its borrowed light. The satellites of other 
planets are from time to time eclipsed in the same way by 
entering the shadows of their primaries ; among these the 
satellites of Jupiter are objects whose eclipses may be 
observed with great regularity. 

The Eakth's Shadow and Penumbra. 

In Fig. 40 let 8 represent the sun, and E the earth. Draw straight 
lines, DBF and D'B'V, each tangent to the sun and the earth. 
The two bodies being supposed spherical, these lines will be the 
intersections of a cone with the plane of the paper, and may be 
taken to represent that cone. It is evident that the cone B VB' will 
be the outline of the shadow of the earth, and that within this cone 
no direct sunlight can penetrate. It is therefore called the earth's 
shadow-eone. 

Let us also draw the lines D'BP and DBF' to represent the 
other cone tangent to the sun and earth. It is then evident that 
within the region VBP and VB' P' the light of the sun will b€> 
partially but not entirely cut off. 



130 



ASTRONOMY. 



Dimensions of Shadow. — Let us investigate the distance E V from 
the centre of the earth to the vertex of the shadow. The triangles 
VEB and VSD are similar, having a right angle at B and at D. 
Hence 

VE:EB= VS:SD = ES: {SB - E B). 

So if we put 

I = YE, the length of the shadow measured from the centre of 
the earth, 
r = ES, the radius-vector of the earth, 
R = SB, the radius of the sun, 
p= EB, the radius of the earth. 



we have 



l=VE = 



ES X EB 
SB - EB 



r p 




Fig. 40.— Form of Shadow. 

That is, I is expressed in terms of known quantities, ^nd thus is 
known. 

The radius of the shadow diminishes uniformly with \\iq distance 
as we go ovitwar(i from the earth. At any distance z from the 

earth's centre it will be ec^ual to il —i)p, for this formula gives 

the radius p when s = 0, and the diameter zero when 2 == Z as it 
should.* 



* It will be noted that this expression is not, rigorously speaking, the semi- 
diameter of the shadow, but the shortest distance from a point on its central 
line to its conical surface. This distance is measured in a direction EB perpen- 
dicular to DB^ whereas the diameter would be perpendicular to the j^xis S Ey^ 
ftftcl its half-length wovil^ V>^ a little greater thac^ EB^ 



ECLIPSES OF THE SUN AND MOON. lai 



Eclipses of the Moon. 

The mean distance of the moon from the earth is about 
60 radii of the latter, and the length E V of the earth's 
shadow is 217 radii of the earth. Hence when the moon 
passes through the shadow she does so at a point less than 
three tenths of the way from E to V. The radius of the 
shadow here will be ^-^-j-^ of the radius E B oi the earth, 
a quantity which we readily find to be about 4600 kilo- 
metres. The radius of the moon being 1736 kilometres, it 
will be entirely enveloped by the shadow when it passes 
through it within 2864 kilometres of the axis E V oi the 
shadow. If its least distance from the axis exceed this 
amount, a portion of the lunar globe will be outside the 
limits BV oi the shadow-cone, and will therefore receive a 
portion of the direct light of the sun. If the least distance 
of the centre of the moon from the axis of the shadow is 
greater than the sum of the radii of the moon and the 
shadow — that is, greater than 6336 kilometres — the moon 
will not enter the shadow at all, and there will be no eclipse 
proper, though the brilliancy of the moon is diminished 
wherever she is within the penumbral region. 

When an eclipse of the moon occurs, the phases are laid down 
in the almanac. (See Fig. 40.) Supposing the moon to be moving 
around the earth from below upward, its advancing edge first 
meets the boundary BP of the penumbra. The time of this 
occurrence is given in the almanac as that of "moon entering 
penumbra." A small portion of the sunlight is then cut off from the 
advancing edge of the moon, and this amount constantly increases 
until the edge reaches the boundary B' V of the shadow. It is 
curious, however, that the eye can scarcely detect any diminution in 
the brilliancy of the moon until she lias almost touched the boundary 
of the shadow. The observer must not, therefore, expect to detect the 
^opiing eclipse until very nearly the time given in the almanac as that 



132 ASTRONOMY. 

of "moon entering shadow." As this happens, the advancing 
portion of the lunar disk will be entirely lost to view, as if it were 
cut off by a rather ill-defined line. It takes the moon about an hour 
to move over a distance equal to her own diameter, so that if the 
eclipse is nearly central the whole moon will be immersed in the 
shadow about an hour after she first strikes it. This is the time of 
beginning of total eclipse. So long as only a moderate portion of 
the moon's disk is in the shadow, that portion will be entirely 
invisible, but if the eclipse becomes total the whole disk of the moon 
will nearly always be plainly visible, shining with a red coppery 
light. This is owing to the refraction of the sun's rays by the lower 
strata of the earth's atmosphere. We shall see hereafter that if a ray 
of light D B passes from the sun to tlie earth, so as just to graze the 
latter, it is bent by refraction more than a degree out of its course, 
so that at the distance of the moon the whole shadow of the earth 
is filled with this refracted light. An observer on the moon would, 
during a total eclipse of the latter, see the earth surrounded by a 
ring of light, and this ring would appear red, owing to the absorp- 
tion of the blue and green rays by the earth's atmosphere, just as the 
sun seems red when setting. 

The moon may remain enveloped in the shadow of the earth 
during a period ranging from a few minutes to nearly two hours, 
according to the distance at which she passes from the axis of the 
shadow and the velocity of her angular motion. When she leaves 
the shadow, the phases which we have described occur in reverse 
order. 

It very often happens that the moon passes through the penumbra 
of the earth without touching the shadow at all. The diminution of 
light in such cases is scarcely perceptible unless the moon at least 
grazes the edge of the shadow. 



Eclipses of the Stjn. 

In Fig. 40 we may suppose B E B' to represent the 
moon. The geometrical theory of the shadow will remain 
the same, though the actual length of the shadow in 
miles will be much less. The mean length of the moon's 
shadow cast by the sun is 377,000 kilometres. This is 
nearly equal to the distance of the moon from the earth 
whew she is in conjanction with the sun. We therefore 



ECLIPSES OF THE SUN AND MOON 133 

conclude that when the moon passes between the earth 
and the sun, the former will be yery near the vertex V of 
the shadow. As a matter of fact, an observer on the 
earth's surface will sometimes pass througli the region 
C V C, and sometimes on the other side of V. 

Now, in Fig. 40, still supposing BEB to be the moon, and 
SD D' to be the sun, let us draw the lines BBV and D'B P tan- 
gent to both moon and sun, but crossing each other between these 
bodies at b. It is evident that an observer outside the space 
PBB'P' will see the whole sun, no part of the moon being project- 
ed upon it; while within this space the sun will be more or less 
obscured. The whole obscured space may be divided into three 
regions, in each of which the character of the phenomenon is dif- 
ferent. 

First, we have the region BVB' forming the shadow-cone proper. 
Here the sunlight is entirely cut off by the moon, and darkness is 
therefore complete, except so far as light may enter by refraction 
or reflection. To an observer at V the moon would exactly cover 
the sun, the two bodies being apparently tangent to each orfher all 
around. 

Secondly, we have the conical region to the right of V between 
the lines B V and 5' F continued. In this region the moon is seen 
wholly projected upon the sun, the visible portion of the latter 
presenting the form of a ring of light around the moon. This ring 
of light will be wider in proportion to the apparent diameter of the 
sun, the farther out we go, because the moon will appear smaller 
than the sun, and its angular diameter will diminish in a more rapid 
ratio than that of the sun. This region is that of annular eclipse, 
because the sun will present the appearance of an annulus or ring of 
light around the moon. 

Thirdly, we have the region PB V and P'B' V, which we notice 
is continuous, extending around the interior cone. An observer 
here would see the moon partly projected upon the sun, and there-, 
fore a certain part of the sun's light would be cut off. Along the 
inner boundary B V and B' V the obscuration of the sun will be 
complete, but the amount of sunlight will gradually increase out to 
the outer boundary B PB P , where the whole sun is visible, This 
region of partial obscuration is called \\\q penumbra. 

To show more clearly the phenomena of solar eclipses, we present 
another figure representing the penumbra pf tUe moon thrown upon 



134 



ASTRONOMY. 



the earth.* The outer of the two circles aS' represents the limb of the 
sun. The exterior tangents which mark the boundary of the shadow 
cross each other at V before reaching the earth. The earth {E) being 
a little beyond the vertex of the shadow, there can be no total eclipse. 
In this case an observer in the penumbral region, CO or DO, will 
see the moon partly projected on the sun, while if he chance to be 
situated at he will see an annular eclipse. To show how this 
is, we draw dotted lines from tangent to the moon. The angle 
between these lines represents the apparent diameter of the moon as 
seen from the earth. Continuing them to the sun, they show the 
apparent diameter of the moon as projected upon the sun. It will 
be seen that, in the case supposed, when the vertex of the shadow 
is between the earth and moon the latter will necessarily appear 




Fig. 41.— Figure op Shadow for Annular Eclipse. 

smaller than the sun, and the observer will see a portion of the solar 
disk on all sides of the moon, as shown in Fig. 42. 

If the moon were a little nearer the earth than it is represented 
in Fig. 41, its shadow would reach the earth in the neighborhood 
of 0. We should then have a total eclipse at each point of the earth 
on which it fell. It will be seen, however, that a total or annular 
eclipse of the sun is visible only on a very small portion of the earth's 
surface, because the distance of the moon changes so little that the 
earth can never be far from the vertex V of the shadow. As the 



* It wilt be noted that all the figures of eclipses are necessarily drawn very 
much out of proportion. Really the sun is 400 times the dist^anpp of the moon, 
which again is 60 times the radius of the earth. But it would b^ entirely im- 
possible to draw a figure of this proportion; we are therefore obliged to 
represent the earth in Fig. 40 as larger than the sun, and the raoOH as nearly 
Jialf way bQtweea th? earth and sun, 



ECLIPSm OF TQE StfN A^D MOON. 



135 



inoon moves around the earth from west to east, its shadow, whether 

the eclipse be total or annular, moves in the same direction. The 

diameter of the shadow at the 

surface of the earth ranges from 

zero to 150 miles. It therefore 

sweeps along a belt of the 

earth's surface of that breadth, 

in the same direction in which 

the earth is rotating. The 

velocity of the moon relative to 

the earth being 3400 kilometres 

per hour, the shadow would 

pass along with tliis velocity if 

the earth did not rotate, but 

owing to the earth's rotation 

the velocity relative to points 

on its surface may range from 

2000 to 3400 kilometres (1200 Fig. 42. -Dark Body op Moon projected 

^^-^ ., , ^ on Sun DURING AN Annular Eclipse. 

to 2100 miles). 

The reader will readily understand that in order to see a total 
eclipse an observer must station himself beforehand at some point of 
the earth's surface over which the shadow is to pass. These points 
are generally calculated some years in advance, in the astronomical 
ephemerides. 




It will be seen that a partial eclipse of the sun may be 
visible from a much larger portion of the earth's surface 
than a total or annular one. The space CD (Fig. 41) over 
which the penumbra extends is generally of about one half 
the diameter of the earth. Roughly speaking, a partial 
eclipse of the sun may sweep over a portion of the earth's 
surface ranging from zero to perhaps one fifth or one sixth 
of the whole. 

There are really more eclipses of the sun than of the 
moon. A year never passes without at least two of the 
former, and sometimes five or six, while there are rarely 
more than two eclipses of the moon, and in many years 
none at all. But at any one place more eclipses of the 



136 A8TR0N0MT, 

moon will be seen than of the sun. The reason of this is 
that an eclipse of the moon is visible over the entire hemi- 
sphere of the earth on which the moon is shining, and as 
it lasts several hours, observers who are not in this hemi- 
sphere at the beginning of the eclipse may, by the earth's 
rotation, be brought into it before it ends. Thus the 
eclipse will be seen over more than half the earth's surface. 
But, as we have just seen, each eclipse of the sun can be 
seen over only so small a fraction of the earth's surface as 
to more than compensate for the greater absolute fre- 
quency of solar eclipses. 




Fig. 43.— Comparison op Shadow and Penumbra op Earth and Moon. A IS 
THE Position op the Moon during a Solar, B during a Lunar, Eclipse. 

It will be seen that, in order to have either a total or 
annular eclipse visible upon the earth, the line joining 
the centres of the sun and moon, being continued, must 
strike the earth. To an observer on this line the centres 
of the two bodies will seem to coincide. An eclipse in 
which this occurs is called a central one, whether it be 
total or annular. Fig. 43 will perhaps aid in giving a 
clear idea of the phenomena of eclipses of both sun and 
moon. 

THE RECURKENCE OF ECLIPSES. 

If the orbit of the moon around the earth were in or near the 
plane of the ecliptic there would be an eclipse of the sun at every 
new moon» and an eclipse of the moon at every full moon. But, 



ECLIPSES OF THE SUJUf AND MOON. 137 

owing to the inclination of the moon's orbit, the shadow and penum- 
bra of the moon commonly pass above or below the earth at the time 
of new moon, while the moon, at her full, commonly passes above 
or below tbe shadow of the earth. It is only when the moon is 
near its node at the moment of new or full moon that an eclipse can 
occur. 

The question now arises, how near must the moon be to its node 
in order that an eclipse may occur ? It is found that If, at the 
moment of new moon, the moon is more than 18° '6 from its node 
no eclipse of the sun is possible, while if it is less than 13°' 7 an 
eclipse is certain. Between these limits an eclipse may occur or fail 
according to the respective distances of the sun and moon from the 
earth. Half way between these limits, or say 16° from the node, it 




Fig. 44.— niustrating lunar eclipse at different distances from the node. The 
dark circles are the earth's shadow, the centre of which is always in the ecliptic 
A B. The moon's orbit is represented by CD. At G the eclipse is central and 
total, at F it is partial, and at E there is barely an eclipse. 



is an even chance that an eclipse will occur; toward the lower limit 
(13° -7) the chances increase to certainty; toward the upper one 
(18° -6) they diminish to zero. The corresponding limits for an 
eclipse of the moon are 9° and 12i° ; that is, if at the moment of full 
moon the distance of the moon from her node is greater than 12i° 
no eclipse can occur, while if the distance is less than 9° an eclipse 
is certain. We may put the mean limit at 11°. Since, in the long- 
run, new and full moon will occur equally at all distances from the 
node, there will be, on the average, sixteen eclipses of the sun to 
eleven of the moon, or nearly fifty per cent more. 

If, at the moment of new moon, the distance of the moon from 
the node is less than 10^ there will be a central eclipse of the sun, 
and if greater than this there will not be such an eclipse. The 



138 ASTRONOMY. 

eclipse limit may range half a degree or more on each side of this 
mean value, owing to the var3dng distance of the moon from the 
earth. Inside of 10° a central eclipse may be regarded as certain, 
and outside of 11" as impossible. 

If the direction of the moon's nodes from the centre of the earth 
were invariable, eclipses could occur only at the two opposite months 
of the year when the sun had nearly the same longitude as one node. 
For instance, if the longitudes of the two opposite nodes were re- 
spectively 54° and 234°, then, since the sun must be within 12° of 
the node to allow of an eclipse of the moon, its longitude would have 
to be either between 42° and 66°, or between 222° and 246°. But 
the sun is within the first of these regions only in the month of May, 
and within the second only during the month of November. Hence 
lunar eclipses could then occur only during the months of May and 
November, and the same would hold true of central eclipses of the 
sun. Small partial eclipses of the latter might be seen occasionally 
a day or two from the beginnings or ends of the above months, but 
they would be very small and quite rare. Now, the nodes of the 
moon's orbit were actually in the above directions in the year 1873. 
Hence during that year eclipses occurred only in May and No- 
vember. We may call these months the seasons of eclipses for 
1873. 

There is a retrograde motion of the moon's nodes amounting to 
19^° in a year. The nodes thus move back to meet the sun in its 
annual revolution, and this meeting occurs about 20 days earlier 
every year than it did the year before. The result is that the season 
of eclipses is constantly shifting, so that each season ranges through- 
out the whole year in 18*6 years. For instance, the season corre- 
sponding to that of November, 1873, had moved back to July and 
August in 1878, and will occur in May, 1882, while that of May, 
1873, will be shifting back to November in 1882. 

It may be interesting to illustrate this by giving the days in which 
the sun is in conjunction with the nodes of the moon's orbit during 
several years. 



Ascending Node. 


Descending Node. 


1879. 


January 24. 


1879. July 17. 


1880. 


January 6. 


1880. June 27. 


1880. 


December 18. 


1881. June 8. 


1881. 


November 30. 


1882. May 20. 


1882. 


November 12. 


1883. May 1. 


1883. 


October 25. 


1884. April 12. 


1884. 


October 8. 


1885. March 25. 



ECLIPSES OF THE SUN AND MOON. 139 

During these years, eclipses of the moon can occur only within 11 
or 12 days of these dates, and eclipses of the sun only within 15 or 
16 days. 

In consequence of the motion of the moon's node, three varying 
angles come into play in considering the occurrence of an eclipse: 
the longitude of the node, that of the sun, and that of the moon. 
One revolution of the moon relatively to the node is accomplished, 
on the average, in 27 • 21222 days. If we calculate the time required 
for the sun to return to the node, we shall find it to be 346-6201 
days. 

Now, let us suppose the sun and moon to start out together from 
a node. At the end of 346*6201 days the sun, having apparently 
performed nearly an entire revolution around the celestial sphere, will 
again be at the same node, which has moved back to meet it. But the 
moon will not be there. It will, during the interval, have passed 
the node 12 times, and the 13th passage will not occur for a week. 
The same thing will be true for 18 successive returns of the sun to 
the node; we shall not find the moon there at the same time with 
the sun; she will always have passed a little sooner or a little later. 
But at the 19th return of the sun and the 242d of the moon, the two 
bodies will be in conjunction within half a degree of the node. We 
find from the preceding periods that 

242 returns of the moon to the node require 6585.357 days. 
19 •• " sun *♦ " " 6585.780 '« 

The two bodies will therefore pass the node within 10 hours of 
each other. This conjunction of the sun and moon will be the 223d 
new moon after that from which we started. Now, one lunation 
(that is, the interval between two consecutive new moons) is, in the 
mean, 29.530588 days; 223 lunations therefore require 6585.32 days. 
The new moon, therefore, occurs a little before the bodies reach the 
node, the distance from the latter being that over which the moon 
moves in 0*^.036, or the sun in 0^.459. This distance is 28' of arc, 
somewhat less than the apparent semidiameter of either body. This 
would be the smallest distance from either node at which any new 
moon would occur during the whole period. The next nearest ap- 
proaches would have occurred at the 35th and 47th lunations respec- 
tively. The 35th new moon would have occurred about 6° before 
the two bodies arrived at the node from which we started, and the 
47th about 1|° past the opposite node. No other new moon would 
AC'ur so near a node before the 223d one, which, as we hare just 
,,»n. would occur 0° 28' west of the node. This period of 223 neW 



140 A&TnONOMY. 

moons, or 18 years 11 days, was called the Saros by the ancient as- 
tronomers, and by means of it they predicted eclipses. 

The possibility of a total eclipse of the sun arises from the occa- 
sional very slight excess of the apparent angular diameter of the 
moon over that of the sun. This excess is so slight that such an 
eclipse can never last more than a few minutes. It may be of inter- 
est to point out the circumstances which favor a long duration of 
totality. These are: 

(1) That the moon should be as near as possible to the earth, or, 
technically speaking, in perigee, because its angular diameter as 
seen from the earth will then be greatest. 

(2) That the sun should be near its greatest distance from the 
earth, or in apogee, because then its angular diameter will be the 
least. It is now in this position about the end of June; hence the 
most favorable time for a total eclipse of very long duration is in the 
summer months. Since the moon must be in perigee and also be- 
tween the earth and sun, it follows that the longitude of the perigee 
must be nearly that of the sun. The longitude of the sun at the 
end of June being 100°, this is the most favorable longitude of the 
moon's perigee. 

(3) The moon must be very near the node in order that the centre 
of the shadow may fall near the equator. The reason of this condi- 
tion is that the duration of a total eclipse may be considerably in- 
creased by the rotation of the earth on its axis. We have seen that 
the shadow sweeps over the earth from west toward east with a 
velocity of about 3400 kilometres per hour. Since the earth rotates 
in the same direction, the velocity relative to the observer on the 
earth's surface will be diminished by a quantity depending on this 
velocity of rotation, and therefore greater the greater the velocity. 
The velocity of rotation is greatest at the earth's equator, where it 
amounts to 1660 kilometres per hour, or nearly half the velocity of 
the moon's shadow. Hence the duration of a total eclipse may, with- 
in the tropics, be nearly doubled by the earth's rotation. When all 
the favorable circumstances combine in the way we have just de- 
scribed, the duration of a total eclipse within the tropics will be 
about seven minutes and a half. In our latitude the maximum du- 
ration will be somewhat less, or not far from six minutes, but it is 
only on very rare occasions, hardly once in many centuries, that all 
these favorable conditions can be expected to concur. 

Occultation of Stars by the Moon. — A phenomenon which, geomet- 
rically considered, is analogous to an eclipse of the sun is the occul- 
tation of a star by the moon. Since all the bodies of the solar system 
are nearer than the fixed stars, it is evident that they must from 



ECLIPSES OE THE SVfN AND MOOK 141 

time to time pass between us and tlie stars. The planets are, how- 
ever, so small that such a passage is of very rare occurrence, and 
when it does happen the star is generally so faint that it is rendered 
invisible by the superior light of the planet before the latter touches 
it. But the moon is so large and her angular motion so rapid that 
she passes over some star visible to the naked eye every few daj^s. 
Such phenomena are termed occultations of stars hy the moon. It 
must not, however, be supposed that they can be observed by the 
naked eye. In general, the moon is so bright that only stars of the 
first magnitude can be seen in actual contact with lier limb, and even 
then the contact must be with the unilluminated limb. 



CHAPTER IX. 

THE EARTH. 

Our object in the present chapter is to trace the effects 
of terrestrial gravitation and to study the changes to which 
it is subject in yarious places. Since every part of the 
earth attracts every other part as well as every object upon 
its surface, it follows that the earth and all the objects 
that we consider terrestrial form a sort of system by them- 
selves, the parts of which are firmly bound together by 
their mutual attraction. This attraction is so strong that 
it is found impossible to project any object from the sur- 
face of the earth into the celestial spaces. Every particle 
of matter now belonging to the earth must, so far as we 
can see, remain upon it forever. 

Mass and Density of the Earth. 

The mass of a body may be defined as the qitantity of 
matter which it cofitams. 

There are two ways to measure this quantity of matter: (1) By 
tlie attraction or weight of the body — this weight being, in fact, tlie 
mutual force of attraction between the body and tlie earth ; (2) By 
the inertia of the body, or the amount of force whicli we must apply 
to it in order to make it move with a definite velocity. Mathemati- 
cally, there is no reason why these two methods should give the same 
result, but by experiment it is found that the attraction of all bodies 
is proportional to their inertia. In other words, all bodies, whatever 
their chemical constitution, fall exactly the same number of feet in 
one second under the influence of gravity, supposing them in a 



THE EARTH. 143 

vacuum and at the same place on the earth's surface. Although the 
mass of a body is most conveniently measured by its weight, yet 
mass and weiglit must not be confounded. 

The tveight of a body is the apparent force ivith ivhich it 
is attracted toward the centre of the earth. 

This force is not the same in all parts of the earth, nor at dif- 
ferent heights above the earth's surface. It is therefore a variable 
quantity, depending upon the position of the body, while the mass 
of the body is something inherent in it, which remains constant 
wherever the body may be taken, even if it is carried through the 
celestial spaces, where its iceiglit would be reduced to almost noth- 
ing. 

The unit of mass which we may adopt is arbitrary. Generally the 
most convenient unit is the weight of a body at some fixed place on 
the earth's surface — the city of Washington, for example. Suppose 
we take such a portion of tlic earth as will weigh one kilogramme in 
Washington; we may then consider the mass of that particular lot of 
earth or rock as tlie unit of mass, no matter to what part of the uni- 
verse we take it. Suppose, also, that we could bring all the matter 
composing the earth to the city of Washington, one unit of mass at 
a time, for the purpose of weighing it, returning each unit of mass to 
its place in the earth immediately after weighing, so that there should 
be no disturbance of the earth itself. The sum-total of the weights 
thus found would be the mass of the earth, and would be a perfectly 
definite quantity, admitting of being expressed in kilogrammes or 
pounds. We can readily calculate the mass of a volume of water 
equal to that of the earth because we know the magnitude of the 
earth in litres, and the mass of one litre of water. Dividing this 
into the mass of the earth, supposing ourselves able to determine 
this mass, and we shall have the specific gravity, or what is more 
properly called the density, of the earth. 

What we have supposed for the earth we may imagine for any 
heavenly body ; namely, that it is brought to the city of Washington 
in small pieces, and there weighed one piece at a time. Thus the 
total mass of the earth or any heavenly body is a perfectly defined 
and determinate quantity. 

It may be remarked in this connection that our units of weight, the 
pound, the kilogramme, etc., are practically units of mass rather than 
of weight. If we should weigh out a pound of tea in the latitude of 
Washington, and then take it to the equator, it would really be less 
heavy at the equator than iu Washington; but if we take a pound 



144 ASTRONOMY. 

weight with us, that also would be lighter at the equator, so that the 
two would still balance each other, and the tea would be still con- 
sidered as weighing one pound. Since things are actually weighed 
in this way by weights which weigh one unit at some definite place, 
say Washington, and which are carried all over the world without 
being changed, it follows that a body which has any given w^eight in 
one place will, as measured in this way, have the same apparent 
weight in any other place, although its real weight will vary. But 
if a spring- balance or any other instrument for determining absolute 
weights were adopted, then we should find that the weight of the 
same body varied as we took it from one part of the earth to another. 
Since, however, we do not use this sort of an instrument in weigh- 
ing, but pieces of metal which are carried about without change, it 
follows that what we call units of weight are properly units of mass. 
Density of the Earth.— We see that all bodies around us tend to fall 
toward the centre of the earth. According to the law of gravitation, 
this tendency is not simply a single force directed toward the centre 
of the earth, but is the resultant of an infinity of separate forces 
arising from the attractions of all the separate parts which compose 
the earth. The question may arise, how do we know that each 
particle of the earth attracts a stone which falls, and that the whole 
attraction does not reside in the centre ? The proofs of this are 
numerous, and consist rather in the exactitude with which the 
theory represents a great mass of disconnected plienomena than in 
any one principle admitting of demonstration. Perhaps, however, 
the most conclusive proof is found in the hbserved fact that masses 
of matter at the surface of the earth do really attract each other as 
required by the law of Newton. It is found, for example, that 
isolated mountains attract a plumb-line in their neighborhood. 

It is noteworthy that though astronomy affords us the 
means of determining with great precision the relative 
masses of the earth, the moon, and all the planets, it does 
not enable us to determine the absolute mass of any hea- 
venly body in units of tlie weights we use on the earth. 
The sun has about 328,000 times the mass of the earth, and 
the moon only -^V ^^ ^^^is mass, but to know the absolute 
mass of either of them Ave must know how many kilo- 
grammes of matter the earth contains. To determine this 
we must know the roea-n density of the earth, and this ia 



THE EARTH. 145 

something about whicli direct observation can give us no in- 
formation, because we cannot penetrate more than an in- 
significant distance into the earth's interior. The only way 
to determine the density of the earth is to find how much 
matter it must contain in order to attract bodies on its sur- 
face with a force equal to their observed weight ; that is, with 
such intensity that at the equator a body shall fall nearly 
five metres in a second. To find this we must know the 
relation between the mass of a body and its attractive 
force. This relation can only be found by measuring the 
attraction of a body of known mass. 

An attempt to do this was made toward the close of the last cen- 
tury, the attracting body selected being Mount Schehallien in Scot- 
land. The volume, V, of the mountain was known by careful topo 
graphical surveys. The specific gravity or density, D, of the rocks 
composing the mountain was determined by experiment. The mass, 
M, of the mountain was VxD; that is, a known quantity. 

A plumb-line set up at the south end of the mountain was attracted 
away from the true vertical toward the mountain; that is, toward 
the north. A plumb-line at the north end of the mountain was 
attracted toward the south. The amounts of these deviations w'cre 
measured, and they were due to the mass of the mountain. Hence a 
measure of its attractive force was obtained. 

The actual process of determining the deviations of the plumb- 
lines N and /S was this: The latiiudes of the stations ^Sand iV^were 
determined. These were nothing but the declinations of the zeniths 
of iVand 8, the zeniths being determined by the directions of plumb- 
lines at each station. The difference of latitudes of N and S by 
astronomical observations was known in arc and therefore in feet. 
If the mountain liad no attraction on the plumb-lines, this differ 
ence in feet would be the same as the distance apart of the two 
stations determined b}^ the topographical survey. But it was differ- 
ent, and the amount of the difference was a measure of the attraction 
of this particular mass. This is the general principle according to 
which the relation of mass and attraction is determined. As the mass 
of the mountain and its attraction was known, the density of the 
whole earth could be determined. The earth's mass {M') was equal 
to.it§ volume (F'} tinges its deosity {D'). Its volume was known, Us 



146 ASTRONOMY. 

mass was known, because it must be such as to attract bodies with 
forces measured by their weights, and hence its density was deter- 
mined from this experiment. The actual result was that the earth 
was 4-7 times as dense as water. Other researches give about 
5-6 for the density of the earth; this is more than double the average 
specific gravity of the rocks which compose the surface of the globe: 
whence it follows that the inner portions of the earth are much more 
dense than the outer parts. 

Laws of Terbestrial Gravitation. 

The earth being very nearly spherical, certain theorems respecting 
the attraction of spheres may be applied to it. The demonstration 
of these theorems requires the use of the Integral Calculus, and will 
be omitted here, only the conditions and the results being stated. 
Let us imagine a hollow shell of matter, of which the internal and 
external surfaces are both spheres, attracting any other mass of 
matter, a small particle we may suppose. This particle will be 
attracted by every particle of the shell with a force inversely as the 
square of its distance from it. The total attraction of the shell will 
be the resultant of this infinity of separate attractive forces. 

Theorem I. — If the particle he outside the shell, it will he attracted 
as if the whole mass of the shell were concentrated in its centre. 

Theorem II. — If the particle he inside the shell, the opposite attrac- 
tions in every direction will neuiralize each other, no matter whereahouts 
in the interior the particle may be, and the resultant attraction of the 
sliell will therefore he zero. 

To apply this to the attraction of a solid sphere, let us first sup- 
pose a body either outside the sphere or on its surface. If we con- 
ceive the sphere as made up of a great number of spherical shells, the 

attracted point will be external to all of 
them. Since each shell attracts as if 
its whole mass were in the centre, it 
follows that the whole sphere attracts 
a body upon the outside of its surface 
as if its entire mass were concentrated 
at its centre. 

Let us now suppose the attracted 
particle inside the sphere, as at P, Fig. 
45. and imagine a spherical surface 
PQ concentric with the sphere and 
passing through the attracted particle. 
Fro. is. All that portion of the sphere lyin^ 




THE EARTH. 147 

outside this spherical surface will be a spherical shell having the 
particle inside of it, and will therefore exert no attraction whatever 
on the particle. That portion inside the surface will constitute a 
sphere with the particle on its surface, and will therefore attract as 
if all this portion were concentrated in the centre. To find what 
this attraction will be, let us first suppose the whole sphere of equal 
density. Let us put 

a, the radius of the entire sphere. 

r, the distance PC of the particle from the centre. 

The total volume of matter inside the sphere P Q will then be, by 

4 
geometry,— 7t 7^. Dividing by the square of the distance r, we see 

o 

that the attraction will be represented by 

4 

that is, inside the sphere tKe attraction will be directly as the dis- 
tance of the particle from the centre. If the particle is at the sur- 

4 
face we have r = a, and the attraction is — ;ra. Outside the sur- 

o 

4 
face the whole volume of the sphere — tt a^ will attract the particle, 

o 

4 a^ 
and the attraction will be -^ ;r — -. If we put ?■ = a in this formula, 

we shall have the same result as before for the surface attraction. 

Let us next suppose that the density of the sphere varies from its 
centre to its surface, so as to be equal at equal distances from the 
centre. We may then conceive of it as formed of an infinity of con- 
centric spherical shells, each homogeneous in density, but not of the 
same density as the others. Theorems I. and II. will then still 
apply, but their result will not be the same as in the case of a homo- 
geneous sphere for a particle inside the sphere. Referring to Fig. 
45, let us put 

B, the mean density of the shell outside the particle P. 
J)', the mean density of the portion P Q inside of P. 

We shall then have : 

4 
Volume of the shell, —7t{a^ — r^). Volume of the inner sphere, 

o 

4 4 

-5 7t ?•». Masa of the shell = vol. X D ^-tc D {a^ — 7-^). Mass of the 

o d 



148 ASTRONOMY. 

4 
inner sphere = vol. X -D' = —tc D'r^, Mass of the whole sphere = 
o 

sum of masses of shell and inner sphere = tt '^ I Z) a^ -f- (Z)' — D) r^\. 

Attraction of the whole sphere upon a point at its surface = 

Attraction of the inner sphere (the same as that of the whole shell) 

. , , n Mass 4 _,, 
upon a pomt at P = — ^— = — TtD r. 

If, as in the case of the earth, the density continually increases to- 
ward the centre, the value of D will increase also, as r diminishes, so 
that gravity will diminish less rapidly than in the case of a homo- 
geneous sphere, and may, in fact, actually increase as we descend. 
To show this, let us subtract the attraction at P from that at the sur- 
face. The difference will give : 

Diminution 2ii P = - n yD a -{- {D' - D) - - D'r\ 

Now let us suppose r a very little less than a, and put r = a — d\ 
d will then be the depth of the particle below the surface. 

Cubing this value of r, neglecting the higher powers of d, and 

dividing by a-, we find —^ = a — 3(f. Substituting in the above 

4 
equation, the diminution of gravity at P becomes -^ it {dD—2'D)d. 

We see that if 3 D < 3 B' — that is, if the density at the surface is 
less than ^ of the mean density of the whole inner mass — this quan- 
tity will become negative, showing that the force of gravity will be 
less at the surface than at a small depth in the interior. But it must 
ultimately diminish, because it is necessarily zero at the centre. It 
was on this principle that Professor Airy determined the density of 
the earth by comparing the vibrations of a pendulum at the bottom 
of the Harton Colliery, and at the surface of the earth in the neigh- 
borhood. At the bottom of the mine the pendulum gained about 
2»-5 per day, showing the force of gravity to be greater there than at 
the surface. 

Figure and Magnitude of the Eabth. 

If the earth were fluid and did not rotate on its axis, it 
would assume the form of a perfect sphere. The opinion 



THE EARTH. 149 

is entertained that the earth was once in a molten state, 
and that this is the origin of its present nearly spherical 
form. If we give such a sphere a rotation upon its axis, 
the centrifugal force at the equator acts in a direction op- 
posed to gravity, and thus tends to enlarge the circle of 
the equator. It is found by mathematical analysis that the 
form of such a revolving fluid sphere, supposing it to be 
perfectly homogeneous, will be an oblate ellipsoid ; that is, 
all the meridians will be equal and similar ellipses, having 
their major axes in the equator of the sphere and their 
minor axes coincident with the axis of rotation. Our earth, 
however, is not wholly fluid, and the solidity of its conti- 
nents prevents its assuming the form it would take if the 
ocean covered its entire surface. By the figure of the 
earth we mean, hereafter, not the outline of the solid and 
liquid portions respectively, but the figure which it would 
assume if its entire surface were an ocean. Let us 
imagine canals dug down to the ocean level in every direc- 
tion through the continents, and the water of the ocean to 
be admitted into them. Then the curved surface touching 
the water in all these canals, and coincident with the sur- 
face of the ocean, is that of the ideal earth considered by 
astronomers. By the figure of the earth is meant the figure 
of this liquid surface, without reference to the inequalities 
of the solid surface. 

We cannot say that this ideal earth is a perfect ellipsoid, 
because we know that the interior is not homogeneous, but 
all the geodetic measures heretofore made are so nearly 
represented by the hypothesis of an ellipsoid that the lat- 
ter is a very close approximation to the true figure. The 
deviations hitherto noticed are of so irregular a character 
that they have not yet been reduced to any certain law. 



150 ASTRONOMY. 

The largest which have been observed seem to be due to 
the attraction of mountains, or to inequalities in the den- 
sity of the rocks beneath the surface. 

Method of Triangulation. — Since it is practically impossi- 
ble to measure around or through the earth, the magnitude 
as well as the form of our planet has to be found by com- 
bining measurements on its surface with astronomical ob- 
servations. Eveii a measurement on the earth's surface 
made in the usual way of surveyors would be impracticable, 
owing to the intervention of mountains, rivers, forests, and 
other natural obstacles. The method of triangulation is 
therefore universally adopted for measurements extending 
over large areas. 




Fig. 46.— a Part of the French Triangulation near Paris. 

Triangulation is executed in the following way : Two points, a 
and b, a few miles apart, are selected as the extremities of a base- 
line. They must be so chosen that their di-tance apart can be accu- 
rately measured by rods ; the intervening ground should therefore 
be as level and free from obstruction as possible. One or more ele- 
vated points, E F, etc., must be visible from one or both ends of the 
base-line. By means of a theodolite and by observation of the pole- 
star, the directions of these points relative to the meridian are accu- 
rately observed from each end of the base, as is also the direction ab 
of the base-line itself. Suppose ^ to be a point visible from each 
epd of tUe base, then Ia the triangle abF y/e have the length ab d^ 



THE EAnTH. 151 

termined by actual measurement, and the angles at a and 6 deter- 
mined by observations. With these data the lengths of the sides 
aF diwd. b Fare determined by a simple computation. 

The observer then transports his instruments to F, and determines 
in succession the direction of the elevated points or hills D E GHJ, 
etc. He next goes in succession to each of these hills, and determines 
the direction of all the others which are visible from it. Thus a net- 
work of triangles is formed, of which all the angles are observed 
with the theodolite, while the sides are successively calculated from 
the first base. For instance, we have just shown how the side aFis 
calculated; this forms a base for the triangle F Fa, the two remain- 
ing sides of which are computed. The side £^^ forms the base of 
the triangle G E F, the sides of which are calculated, etc. In this 
operation more angles are observed than are theoretically necessary 
to calculate the triangles. This surplus of data serves to insure the 
detection of any errors in the measures, and to test iheir accuracy by 
the agreement of their results. Accumulating errors are further 
guarded against by measuring additional sides from time to time as 
opportunity offers. 

Chains of triangles have thus been measured in Russia and Sweden 
from the Danube to the Arctic Ocean, in England and France from 
the Hebrides to Algiers, in this country down nearly our entire At- 
lantic coast and along the great lakes, and through shorter distances 
in many other countries. An east and west line is now being run 
by the Coast Survey from the Atlantic to the Pacific Ocean. Indeed 
it may be expected that a network of triangles will be gradually ex- 
tended over the surface of every civilized country, in order to con- 
struct perfect maps of it. 

Suppose that we take two stations, a and J, Fig. 46, situated north 
and south of each other, determine the latitude of each, and calculate 
the distance between them by means of triangles, as in the figure. 
It is evident that by dividing the distance in kilometres by the dif- 
ference of latitude in degrees we shall have the length of one degree 
of latitude. Then if the earth were a sphere, we should at once have 
its circumference by multiplying the length of one degree by 860. 
It is thus found that the length of a degree is a little more than 111 
kilometres, or between 69 and 70 English statute miles. Its circum- 
ference is therefore about 40,000 kilometres, and its diameter between 
12,000 and 13,000.* 

* "\^Tien the metric system was originally designed by the French, it was in- 
tended that the kilometre should be i^hm of the distance from the pole of the 
earth to the equator. This would make a degree of the meridian equal, on the 
average, to 111^ kilometres. But the metre actually adopted is nearly ^ of 
an inch too shdrt. 



im 



ASmowoMT. 



Owing to the ellipticity of the earth, the length of one degree 
varies with the latitude and the direction in which it is measured. 
The next step in the order of accuracy is to find the magnitude and 
the form of the earth from measures of long arcs of latitude (and 
sometimes of longitude) made in different regions, especiallj^ near 
the equator and in high latitudes. But we shall still find that dif- 
ferent combinations of measures give slightly different results, both 
for the magnitude and the ellipticity, owing to the irregularities in 
the direction of attraction which we have already described. The 
problem is therefore to find what ellipsoid will satisfy the measures 
with the least sum-total of error. New and more accurate solutions 
will be reached from time to time as geodetic measures are extended 
over a wider area. The following are among the most recent results: 




Fig. 47. 

the earth's polar semidiameter, 6355-270 kilometres; earth's equatorial 
semidiameter, 6377-377 kilometres ; earth's compression, -g^i^.^ of the 
equatorial diameter ; earth's eccentricity of meridian, 0-08319. An- 
other result is that of Captain Clarke of England, who found: 
polar semidiameter, 6356-456* kilometres; equatorial semidiameter, 
6378-191 kilometres. 

Geographic and Geocentric Latitudes. — An obvious result of the 
ellipticity of the earth is that the plumb-line does not point toward 
the earth's centre. Let Fig. 47 represent a meridional section of the 
earth, NS being the axis of rotation, E Q the plane of the equator, 
and the position of the observer. The line HE, tangent to the 



* Captain Clarke's results are given in feet, the polar radius being 20,854,895 
feet, the equatorial 20,926,202. These numbers are in the proportion 292 : 293. 



TUB EAItTB. 153 

earth at 0, will then represent the horizon of the observer, -while the 
\me ZN\ perpendicular to II R, aud therefore normal to the earth 
at 0, will be the vertical as determined by the plumb-line. The angle 
ON'Q, or ZO ^', which the observer's zenith makes with the equa- 
tor will then be his astronomical or geographical latitude. This is 
the latitude which in practice we always have to use, because we 
are obliged to determine latitude by astronomical observation, and 
not by measurement from the equator. We cannot determine the 
direction of the true centre C of the earth by direct observation of 
any kind, but only the direction of the plumb-line, or of the perpen- 
dicular to a fluid surface. Z 0^' is the astronomical latitude. If, 
however, we conceive the line COz drawn from the centre of the 
earth through 0, z will be the observer's geocentric zenith, while the 
angle C Q will be his geocentric latitude. It will be observed that it 
is the geocentric and not the geographic latitude which gives the true 
position of the observer relative to the earth's centre. The difference 
between the two latitudes is the angle CON' or ZOz ; tiiis is called 
the angle of the vertical. It is zero at the poles and at the equator, be- 
cause here the normals pass tlirough the centre of the ellipse, and it 
attains its maximum of 11' 30" at latitude 45°. It will be seen that the 
geocentric latitude is always less than the geographic. In north 
latitudes the geocentric zenith is south of the apparent zenith, and in 
southern latitudes north of it; being nearer the equator in each case. 



Motion of the Earth's Axis, or Precession of the 
Equinoxes. 

Sidereal and Equinoctial Year. — In describing theappar- 
, ent motion of the sun, two ways of finding the time of its 
apparent revolution around the sphere were described ; in 
other words, of fixing the length of a year. One of these 
methods consists in finding the interval between successive 
passages of the sun through the equinoxes, or, which is the 
same thing, across the plane of the equator, and the other 
by finding when it returns to the same position among the 
stars. Two thousand years ago Hipparchus found, by 
comparing his own observations with those made two cen- 
turies before by Timocharis, that these two methods pf 



154 ASTRONOMY, 

fixing the length of the year did not give the same result. 
It had previously been considered that the length of a year 
was about 365|: days, and in attempting to correct this 
period by comparing his observed times of the sun's pass- 
ing the equinox with those of Timocharis, Hipparchus 
found that the length required a diminution of seven or 
eight minutes. He therefore concluded that the true length 
of the equinoctial year was 365 days 5 hours and about 53 
minutes. When, however, he considered the return of the 
sun not to the equinox, but to the same position relative 
to the bright star Spica Virginis, he found that it took 
some minutes more than 365^ days to complete the revolu- 
tion. Thus there are two years to be distinguished, the 
tropical or equinoctial year and the sidereal year. The 
first is measured by the time of the sun's return to the 
equinox ; the second by its return to the same position 
relative to the stars. Although the sidereal year is the 
correct astronomical period of one revolution of the earth 
around the sun, yet the equinoctial year is the one to be 
used in civil life, because the change of seasons depends 
upon that year. Modern determinations show the respec- 
tive lengths of the two years to be : 

Sidereal year, 365^ 6^ 9™ 9^ = 365<^. 25636. . 

Equinoctial year, 365*^ 5^» 48°^ 46^ = 365^.24220. . 

It is evident from this difference between the two years 
that the position of the equinox among the stars must be 
changing, and that it must mbve toward the west, because 
the equinoctial year is the shorter. This motion is called 
the precession of the equinoxes, and amounts to about 50" 
per year. The equinox being simply the point in which 
the equator and the ecliptic intersect, it is evident that it 



THE EABTH. 155 

can change only through a change in one or both of these 
circles. Hippaechus found that the change was in the 
equator and not in the ecliptic, because the declinations 
of the stars changed, while their latitudes did not. Since 
the equator is defined as a circle everywhere 90° distant 
from the pole, and since it is moving among the stars, it 
follows that the pole must also be moving among the stars. 
But the pole is nothing more than the point in which the 
earth's axis of rotation intersects the celestial sphere: the 
position of this pole in the celestial sphere depends solely 
upon the direction of the earth's axis, and is not changed by 
the motion of the earth around the sun. Hence precession 
shows that the direction of the earth's axis is continually 
changing. Careful observations from the time of Hippar- 
CHUS until now show that the change in question consists 
in a slow revolution of the pole of the earth around the pole 
of the ecliptic as projected on the celestial sphere. The 
rate of motion is such that the revolution will be completed 
in between 25,000 and 26,000 years. At the end of this 
period the equinox and solstices will have made a complete 
revolution in the heavens. 



The nature of this motion will be seen more clearly by referring to 
Fig. 32, p. 93. We have there represented the earth in four posi- 
tions during its annual revolution. We have represented the axis aa 
inclining to the right in each of these positions, and have described 
it as remaining parallel to itself during an entire revolution. The 
phenomena of precession show that this is not absolutely true, but 
that, in reality, the direction of the axis is slowly changing. This 
change is such that, after the lapse of some 6400 years, the north 
pole of the earth, as represented in the figure, will not incline to the 
right, but toward the observer, the amount of the inclination remain- 
ing nearly the same. The result will evidently be a shifting of the 
seasons. At D we shall have the winter solstice, because the north 
pole will be inclined toward the observer and therefore from the sun, 



156 ASmoNOMY. 

while at A we shall have the vernal equinox instead of the winter 
solstice, and so on. 

In 6400 years more the north pole will be inclined toward the left, 
and the seasons will be reversed. Another interval of the same 
length, and the north pole will be inclined from the observer, the 
seasons being shifted through another quadrant. Finally, at the 
end of about 25,800 years, the axis will have resumed its original 
direction. 

Precession thus arises from a motion of the earth alone and not of 
the heavenly bodies. Although the direction of the earth's axis 
changes, yet the position of this axis relative to the crust of the earth 
remains invariable. Some have supposed that precession would 
result in a change in the position of the north pole on the surface of 




Fig. 48. 

the earth, so that the northern regions would be covered by the 
ocean as a result of the different direction in which the ocean would 
be carried by the centrifugal force of the earth's rotation. This, how- 
ever, is a mistake. It has been shown that the position of the poles, 
and therefore of the equator, on the surface of the earth, cannot 
change except from some variation in the arrangement of the earth's 
interior. Scientific investigation has yet shown nothing to indicate 
any probability of such a change. 

The motion of precession is not uniform, but is subject to several 
small inequalities which are called nutation. 



The Cause of Precession. 

The cause of precession, etc., is illustrated in the figure, which 
shows a spherical earth surrounded by a ring of matter at the eqija- 
tor. If the earth were really spherical there would be no precession. 
It is, however, ellipsoidal with a protuberance at the equator. The 



THE EAHTH. 157 

effect of this protuberance is to be examined. Consider the action 
between the sun and earth alone. If the ring of matter were absent, 
the earth would revolve about the sun as is shown in Fig. 32, p. 93 
(Seasons). 

We remember that the sun's N. P. D. is 90° at the equinoxes, and 
66i° and 113^° at the solstices. At the equinoxes the sun is in the 
direction Cm; that is, NCm is 90°. At the winter solstice the sun is 
in the direction Cc ; NCc = 1131°. It is clear that in the latter case 
the effect of the sun on the ring of matter will be to pull it down 
from the direction Cm towards the direction Gc. An opposite effect 
will be produced by the sun when its polar distance is 66i°. 

The moon also revolves round the earth in an orbit inclined to the 
equator, and in every position of the moon it has a different action 
on the ring of matter. The earth is all the time rotating on its axis, 
and these varying attractions of sun and moon are equalized and 
distributed since different parts of the earth are successively presented 
to the attracting body. The result of all the complex motions we 
have described is a conical motion of the earth's axis JS C about the 
line CE. 

The eartTi's shape is not that given in the figure, but it is an ellip- 
soid of revolution. The ring of matter is not confined to the equator, 
but extends away from it in both directions. The effects of the 
forces acting on the earth as it is are however, similar to the effects 
we have described. 



CHAPTER X. 
CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. 

The Celestial Scale of Measurement. 

The units of length and mass employed by astronomers 
are necessarily different from those used in daily life. The 
distances and magnitudes of the heavenly bodies are never 
reckoned in miles or other terrestrial measures for astro- 
nomical purposes; when so expressed it is only for the pur- 
pose of making the subject clearer to the general reader. 
The units of weight or mass are also, of necessity, astro- 
nomical and not terrestrial. The mass of a body may be 
expressed in terms of that of the sun or of the earth, but 
never in kilogrammes or tons, unless in popular language. 
There are two reasons for this course. One is that in most 
cases celestial distances have first to be determined in 
terms of some celestial unit — the earth's distance from the 
sun, for instance — and it is more convenient to retain this 
unit than to adopt a new one. The other is that the 
values of celestial distances in terms of ordinary terrestrial 
units are for the most part uncertain, while the corre- 
sponding values in astronomical units are known with 
great accuracy. 

An extreme instance of this is afforded by the dimensions 
of the solar system. By a series of astronomical observa- 
tions, investigated by means of Kepler's laws and the 
theory of gravitation, it is possible to determine the forms 



MEASUREMENTS OF MASS AND DISTANCE. 159 

of the planetary orbits, their positions, and their dimen- 
sions in terms of the earth's mean distance from the sun 
as the unit of measure, with great precision. Kepler's 
third law enables us to determine the mean distance of a 
planet from the sun when we know its period of revolu- 
tion. All the major planets, as far out as Saturn, have been 
observed through so many revolutions that their periodic 
times can be determined with great exactness — in fact 
within a fraction of a millionth part of their whole amount. 
The more recently discovered planets, Uranus and Nep- 
tune, will, in the course of time, have their periods deter- 
mined with equal precision. Then, if we square the peri- 
ods expressed in years and decimals of a year, and extract 
the cube root of this square, we have the mean distance 
of the planet with the same order of precision. This 
distance is to be corrected slightly in consequence of the 
attractions of the planets on each other, but these correc- 
tions also are known with great exactness. Again, the 
eccentricities of the orbits are exactly determined by care- 
ful observations of the positions of the planets during suc- 
cessive revolutions. Thus we could make a map of the 
planetary orbits so exact that the error would entirely 
elude the most careful scrutiny, though the map itself 
might be many yards in extent. 

On the scale of this same map we could lay down the 
magnitudes of the planets with as much precision as our 
instruments can measure their angular semidiameters. 
Thus we know that the mean diameter of the sun, as seen 
from the earth, is 32'; hence we deduce from formulae 
already given on pages 5 and 57 that the diameter of the 
sun is .0093083 of the distance of the sun from the earth. 
We cau therefore, on our supposed map of the solar system^ 



160 ASTRONOMY. 

lay down the sun in its true size, according to the scale of 
the map, from data given directly by observation. In the 
same way we can do this for each of the planets, the earth 
and moon excepted. There is no immediate and direct 
way of finding how large the earth or moon would look 
from a planet; whence the exception. 

But without further special research into this subject, 
we shall know nothing about the scale of our map. That 
is, we have no means of knowing how many miles or kilo- 
metres correspond in space to an inch or a foot on the map. 
It is clear that in order to fix the distances or the magni- 
tudes of the planets according to any terrestrial standard, 
we must know this scale. Of course if we can learn either 
the distance or magnitude of any one of the planets laid 
down on the map, in miles or in semidiameters of the 
earth, we shall be able at once to find the scale. But this 
process is so difficult that the general custom of astrono- 
mers is not to attempt to use a scale of miles, but to employ 
the mean distance of the sun from the earth as the unit in 
celestial measurements. Thus, in astronomical language, 
we say that the distance of Mercury from the sun is 0.387, 
that of Venus 0.7-^3, that of Mars 1.523, that of Saturn 
9.539, and so on. But this gives us no information respect- 
ing the distances and magnitudes in terms of terrestrial 
measures. The unknown quantities of our map are the 
magnitude of the earth and its distance from the sun in 
terrestrial units of length. Could we only take up a point 
of observation on the sun or a planet, and determine ex- 
actly the angular magnitude of the earth as seen from that 
point, we should be able to lay down the earth of our map 
in its correct size. Then, since we already know the size 
of the earth in terrestrial units from geodetic surveys we, 



MEASUREMENTS OF MASS AND DISTANCE. 161 

should be able to find the scale of our map, and thence 
the dimensions of the whole system in terms of those 
units. 

It -v^ill be seen that what the astronomer really wants is 
not so much the dimensions of the solar system in miles as 
to express the size of the earth in celestial measures. 
This, however, amounts to the same thing, because having 
one, the other can be readily deduced from the known 
magnitude of the earth in terrestrial measures. 

The magnitude of the earth is not the only unknown 
quantity on our map. From Kepler's laws we can deter- 
mine nothing respecting the distance of the moon from the 
earth, because unless a change is made in the units of time 
and space, they apply only to bodies moving around the 
sun. We must therefore determine the distance of the 
moon as well as that of the sun to be able to complete our 
map on a known scale of measurement. 

Measures of the Sqlae and Lunar Parallax. 

The problem of distances in the solar system is reduced 
by the preceding considerations to measuring the distances 
of the sun and moon in terms of the earth's radius. The 
most direct method of doing this is by determining their 
respective parallaxes, which we have shown to be the same 
as the earth's angular semidiameter as seen from them. 
In the case of the sun, the required parallax can be deter- 
mined as readily by measuring the parallaxes of any of the 
planets as by measuring that of the sun, because any one 
measured distance on the map will give us the scale of our 
map. Now, the planets Venus and Mars occasionally 
come much nearer the earth than the sun ever does, and 
tbeir parallaxes also admit of more exact measurement. 



162 ASTRONOMY. 

The parallax of the sun is therefore determined not by ob- 
servations on the sun itself, but on these two planets. 

The general principles of the method of determining the 
parallax of a planet by simultaneous observations at distant 
stations will be seen by referring to the figure. If two 
observers, situated at 8' and S", make a simultaneous 
observation of the direction of the body P, it is evident 
that the solution of a plane triangle will give the distance 
of P from each station. In practice, however, it would 




Fig. 49. 

be impracticable to make simultaneous observations at 
distant stations; and as the planet is continually in motion, 
the problem is a much more complex one than that of 
gimply solving a triangle. 

This is the method of determining the parallax of the 
moon. Knowing the actual figure of tlie earth, observa- 
tions of the moon made at stations widely separated in 
latitude, as Paris and the Cape of Good Hope, can be com- 
bined so as to give the parallax of the moon and thus its 
distance. On precisely the same principles the parallaxes 
of Venus or Mars have been determined. 



MEASUREMENTS OF MASS AND DISTANCE. 163 

Solar Parallax from Transits of Venus. — When Venus is at her in- 
ferior conjunctions she is between tlic sun and the earth. If the 
orbit of Venus lay in the ecliptic, she would be projected on the 
sun's disli at every inferior conjunction. The inclination of her 
orbit is, however, about 3|°, and thus tlie transits oi Venus occur only 
when Venus happens to be near the node of her orbit at the time of 
inferior conjunction. ' When this occurs she is seen to pass across 
the sun's disk. In the last figure, if P is the place of Venus at such 
a time, and if the disk of the sun is PP", then an observer at S". 
will see Venus at P" and one at S' will see her at P. The distance 
P'P" can be measured directly, or it can be calculated by observing 
the time required for Venus to pass across the chord of the sun's 
disk at P' and across the chord at P' . It is obvious that these 
chords are of different length. 

The parallax of Venus {n') is the angle subtended by the earth's, 
radius at P\ the parallax of the sun {tc) is the angle subtended by the 
earth's radius at Pi, 

If a is the distance of the earth from Venus, and if & is the distance 
of the earth from the sun, we know that the earth's radius c will sub- 
tend an angle at Venus of — = it' , and at the sun of — = tt (see .page 
a 

5). That is/c = an' = hit and it' = —-it. 5 is 1' GO; and a is 

a 

about 0.36 at the time of a transit. Hence n' ■=. 3.8;r. 

What we really measure is the difference of the parallaxes n^ ^nd 

It, and thus, by employing the transit of Venus to measure the sun's 

parallax (8".8), we are enabled to use an angle 2.8 times as large, or 

about 25". Even this is a very difl[icult matter: it is hardly possible 

by any one set of measurcsof the solar parallax to determine the latter 

without an uncertainty of ^^^ of its whole amount. In the distance 

of the sun this corresponds to an uncertainty of nearly half a million 

of miles. Astronomers have therefore sought for other methods of 

determining the sun's distance. Although some of these may be 

a little more certain than measures of para,,llax, there is none by 

which the distance of the sun in miles can be determined with any 

approximation to the accuracy which characterizes other celestial 

measures. , ^ 

-Other Methods of Determining Solar Parallax. — A very 
interesting and probably the most accurate metHod of 
measuring the sun's distance depends upon a knowledge of 
the velocity of light. We shall hereafter see that the time 



164 ASTRONOMY. 

required for light to pass from the sun to the earth is known 
with considerable exactness, being very nearly 498 seconds. 
This time can be determined still more accurately. If 
then we can determine experimentally how many miles or 
kilometres light moves in a second, we shall at once have 
the distance of the sun by multiplying that quantity by 
498. The velocity of light is about 300,000 kilometres 
per second. This distance would reach about eight times 
around the earth. It is seldom possible to see two points 
on the earth's surface more than a hundred kilometres 
apart, and distinct vision at distances of more than twenty 
kilometres is rare. Hence to determine experimentally the 
time required for light to pass between two terrestrial sta- 
tions requires the measurement of an interval of time 
which, even under the most favorable cases, can be only a 
fraction of a thousandth of a second. Methods of doing 
it, however, have been devised, and the velocity of light 
would seem to be about 299,900 kilometres per second. 
Multiplying this by 498, we obtain 149,350,000 kilometres 
(a little less than 93,000,000 miles) for the distance of the 
sun. The time required for light to pass from the sun to 
the earth is still uncertain by nearly a second, but this 
value of the sun's distance is probably the best yet ob- 
tained. The corresponding value of the sun's parallax is 
8'.81. 

Yet other methods of determining the sun's distance 
are given by the theory of gravitation. It is found Tby 
mathematical investigation that the motion of the moon is 
subject to several inequalities, having the sun's horizontal 
parallax as a factor. If the position of the moon could be 
determined by observation with the same exactness that 
th§ position of ^ ptar or planet can (whioh it oajinot be). 



MEASUREMENTS OF MASS AND DISTANCE. 165 

this would probably afford the most accurate method of 
determining the solar parallax. 

Brief History of Determinations of the Solar Parallax. — The determi- 
nation of the distance of the sun must at all limes have been one of 
the most interesting scientific problems presented to the human mind. 
The first known attempt to effect a solution of the problem was made 
by Aristarchus, who flourished in the third centuiy before Christ. 
It was founded on the principle that the time of the moon's first 
quarter will vary with the ratio between the distance of the moon 
and sun, which may be shown as follows. In Fig. 50 let ^represent 
the earth, M the moon, and S the sun. Since the sun always 
illuminates one half of the lunar globe, it is evident that when one 




Fig. 50. 

half of the moon's disk appears illuminated the triangle E MSmxiSii 
be right angled at M. Tlie angle ME S can be determined by 
measurement, being equal to the angular distance between the sun 
and the moon. Having two of the angles, the third can be deter- 
mined, because the sum of the three must make two right angles. 
Thence we shall have the ratio between E*^, the distance of the moon, 
and E8, the distance of the sun, by a trigonometrical computation. 
Then knowing the distance of the moon, which can be determined 
with comparative ease (see page 162), we have the distance of the sun 
by multiplying by this ratio. Aristarchus concluded, from his 
supposed measures, that the angle M E S was three degrees less than 

a right angle. We should then have -=-^-- = — - very nearly, since 3' 

ji o ly 

is yV of 57° and ES = 57° (see page 5). It would follow from this 

that the sun was 19 times the dist^pc§ of tJie moon, We now know 



166 ASTRONOMY. 

that this result is entirely wrong, and that it is so because it is im- 
possible to determine the time when the moon is exactly half illumi- 
nated With any approach to the accuracy necessary in the solution of 
the problem. In fact, the greatest angular distance of the earth and 
moon, as seen from the sun — that is, the angle E 8M—\s only about 
one quarter the angular diameter of the moon as seen from the 
earth. 

The second attempt to determine the distance of the sun is men- 
tioned by Ptolemy, though Hippakchus may be the real inventor 
of it. It is founded on a somewhat complex geometrical construc- 
tion of a total eclipse of the moon. It is only necessary to state the 
result, which was that tlie sun was situated at the distance of 1210 
radii of the earth. This result, like the former, was due only to 
errors of observation. So far as all the methods known at the time 
could show, the real distance of the sun appeared to be infinite; 
nevertheless Ptolemy's result was received without question for 
fourteen centuries. 

The first really successful measure of the parallax of a planet was 
made upon Mars during the opposition of 1672, by the first of the 
two methods already described. An expedition was sent to the 
colony of Cayenne to observe the declination of the planet from 
night to night, while corresponding observations were made at the 
Paris Observatory. From a discussion of these observations, Cas- 
siNi obtained a solar parallax of 9". 5, which is within a second of 
the truth. The next steps forward were made by the transits of 
Venus in 1761 and 1769. The leading civilized nations caused obser- 
vations on these transits to be made at various points on the globe. 
The method used was very simple, consisting in the determination 
of the times at which Venus entered upon the sun's disk and left it 
again. The absolute times of ingress and egress, as seen from differ- 
ent points of the globe, might differ by 20 minutes or more on ac- 
count of parallax. Tiie results, however, were found to be discord- 
ant. It was not until more than half a century had elapsed that the 
observations were systematically calculated by Encke of Germany, 
who concluded that the parallax of the sun was 8" .578, and the dis- 
tance 95 millions of miles. 

In 1854 it began to be suspected that Encke's value of the parallax 
was much too small. Hansen, from the theory of the moon, found 
the parallax of the sun to be S".916. This result seemed to be con- 
firmed by other observations, especially those of Mars during 1862. 
It was therefore concluded that the sun's parallax was probably be- 
tween 8". 90 and 9". 00. Subsequent researches have, however, been 
diminishing this value. In 1867, from a discussiou of all the data 



MEASUREMENTS OF MASS AND DISTANCE. 167 

which were considered of value, it was concluded by one of the 
writers that the most probable parallax was 8". 848. The measures 
of the velocity of light reduce this value to 8". 81, and it is now 
doubtful whether the true value is any larger than this. 

All we can say at present is that the solar parallax is probably be- 
tween 8". 79 and 8". 83, or, if outside these limits, that it can be very 
little outside. 

Relative Masses of the Sun and Planets. 

In estimating celestial masses as well as distances, it is necessary 
to use what we may call celestial units; Ihtit is, to take the mass of 
some celestial body as a unit, instead of any multiple of the pound or 
kilogram. The reason of this is that the ratios between the masses 
of the planetary system, or, whicii is the same thing, the mass of 
each body in terms of that of some one body as the unit, can be de- 
termined independently of the mass of any one of them. To express 
a mass in kilogrammes or other terrestrial units, it is necessary to find 
the mass of the earth in such units, as already explained. This, 
however, is not necessary for astronomical purposes, where only the 
relative masses of the several planets are required. In estimating 
the masses of the individual planets, that of the sun is generally 
taken as a unit. The planetary masses will then all be very small 
fractions. 

The mass of the sun being 1.00, the mass of .Verciiri/ is ^j^Tj^xnyTrJ 



Venvs 


is iYZ^JTS'f 


Earth 


js S^UTi; 


Mars 


is sTJ^irTJTT 


Jupiter 


iSxA?; 


Saturn 


js^ii^; 


Uranus 


is 52Ud» 



Neptune is y^^^. 

Masses of the Earth and Sun. — The mass of the earth is connected 
by a very curious relation with the parallax of the sun. Knowing 
the latter, we can determine the mass of the sun relative to the earth, 
which is the same thing as determining the astronomical mass of the 
earth, that of the sun being unity. This may be clearly seen by re- 
flecting that when we know the radius of the earth's orbit we can 
determine how far the earth moves aside from a straight line in one 
second in consequence of the attraction of the sun. This motion 
measures the attractive force of the sun at the distance of the earth. 



168 



ASTRONOMY. 



Comparing it with the attractive force of the earth, and making 
allowance for the difference of distances from centres of the two 
bodies, we determine the ratio between their masses. 

Tbe following table shows, for different values of the solar paral- 
lax, the corresponding ratio of the masses, and distance of the sun in 
terrestrial measures : 







Distance of the Sun 


Solar 


M 








Parallax. 










P" 


m 


In equatorial 

radii of the 

earth. 


In millions of 
miles. 


In millions of 
kilometres. 


8". 77 


335684 


23519 


93 . 208 


150.001 


8". 78 


334538 


23492 


93 . 102 


149 . 830 


8". 79 


333398 


23466 


93 . 996 


149.660 


8". 80 


332263 


23439 


92 . 890 


148 . 490 


8". 81 


331132 


23413 


93.785 


149.320 


8". 83 


330007 


23386 


93.680 


149.151 


8". 83 


328887 


23360 


92.575 


148.983 



We have said that the solar parallax is probably contained between 
the limits 8". 79 and 8". 83. It is certainly hardly more than one or 
two hundredths of a second without them. So, if we wish to ex- 
press the constants relating to the sun in round numbers, we may 
say that — 

Its mass is 330,000 times that of the earth. 

Its distance in miles is 93 millions, or perhaps a little less. 

Its distance in kilometres is probably between 149 and 150 mil- 
lions. 



CHAPTER XL 

THE REFRACTION AND ABERRATION OF LIGHT AND 
TWILIGHT. 

Atmospheeic Refeaction. 

When we speak of the place of a planet or star, we usu- 
ally mean its true place; i.e., its direction from an ob- 
server situated at the centre of the earth. We have shown 
in the section on parallax how observations which are 
necessarily taken at the surface of the earth are reduced 
to what they would have been if the observer were situated 
at the earth's centre. We have supposed the star to be 
projected on the celestial sphere in the prolongation of 
the line joining the observer and the star. The ray from 
the ^tar was considered to suffer no deflection in passing 
through the stellar spaces and through the earth's atmos- 
phere. But from the principles of physics, we know that 
such a luminous ray passing from an empty space (as the 
steUar spaces probably are), and through an atmosphere, 
must suffer a refraction, as every ray of light is known to 
do in passing from a rare into a denser medium. As we 
flee the star in the direction in which its light enters the 
eye — 'that is, as we project the star on the celestial sphere 
by prolonging this light-beam backward into space — -there 
must be an apparent displacement of the star from refrac- 
tion. 

We may recall a few definitions from physics. The ray which 
leaves the star and impinges on the outer surface of the earth's at- 



170 



ASTRONOMY. 



mosphere is called the incident ray ; after its deflection by the atmos- 
phere it is called the refracted ray. The difference between these 
directions is called the astronomical refraction. If a normal is drawn 
(perpendicular) to the surface of the refracting medium at the point 
where the incident ray meets it, the acute angle between the incident 
ray and the normal is called the angle of incidencCy and the acute angle 

between the normal and the refracted 
ray is called the angle of refraction. 
The refraction itself is the difference 
of these angles. The normal and 
both incident and refracted rays are 
in the same vertical plane. In Fig. 
51, SA is the ray incident upon the 
surface BA of the refracting medium 
B BAN, AC is, the refracted ray, 
i»/iV^ the normal, ^ J. 1/ and CAN 
the angles of incidence and refrac- 
tion respectively. Produce CA back- 
ward in the direction AS': SAS' is 
the refraction. An observer at (7 will 
see the star S as if it were at S'. AS is the apparent direction of 
the ray coming from the star 8, and S is the apparent place of the star 
as affected by refraction. 




Fig. 51.— Refraction. 



This explanation supposes the space above B B^ in the 
figure to be entirely empty, and the earth's atmosphere,, 
equally dense throughout, to fill the space hoiovr B B'. 
In fact, however, the earth's atmosphere is most dense 
at the surface of the earth, and gradually diminishes. in 
density to its exterior boundary. Therefore we must sup- 
pose the. atmosphere to be divided into a great number of 
parallel layers of air, and by assuming an infinite num^ 
ber of these we may also assume that throughout each one 
of them the air is equally dense. Hence the precediiig 
figure will only represent the refraction at a single one of 
these layers. The path of a ray of light through the at? 
mosphere is not a straight line like A C, but a curve, "^e 
may suppose this curve to be represented in Fig. 52, where 



REFRACTION AND ABERRATION OF LIGHT 171 

the number of layers lias been taken very small to avoid 
confusing the drawing. 

Let C be the centre and A a point of the surface of the 
earth; let >S' be a star, and Se v^ ray from the star which is 
refracted at the various layers into which we suppose the 
atmosphere to be divided, and which finally enters the eye 
of an observer at ^ in the apparent direction S'A. He 




Fig. 52.— Refraction of Layers of Air. 

will then see the star in the direction S' instead of that of 
yiS', and SA8', the refraction, will throw the star nearer 
to his zenith Z. 

The angle 8' A Z is the apparent zenith distance of S; 
the true zenith distance of S \^ Z A S, and ;iS'^ may be 
assumed to coincide with S e, as for all heavenly bodies 
except the moon it practically does. The line 8e pro- 



172 ASTRONOMY. 

longed will meet the line A Z in & point above A, suppose 

at y. 

Quantity and Effects of Refraction. — At the zenith the 
refraction is 0, at 45° zenith distance the refraction is about 
1', and at 90° it is 34' 30"; that is, bodies at the zenith 
distances of 45° and 90° appear elevated above their true 
places by 1' and 34^' respectively. If the sun has just 
risen — that is, if its lower limb is just in apparent contact 
with the horizon — it is in fact entirely below the true 
horizon, for the refraction (35') has elevated its centre by 
more than its whole apparent diameter (33'). 

The moon is full when it is exactly opposite the sun, 
and therefore, were there no atmosphere, moon-rise of a 
full moon and sunset would be simultaneous. In fact, 
both bodies being elevated by refraction, we see the full 
moon risen before the sun has set. On April 20th, 1837, 
the full moon rose eclipsed before the sun had set. 

Twilight, 

It is plain that one effect of refraction is to lengthen the 
duration of daylight by causing the sun to appear above 
the horizon before the time of his geometrical rising and 
after the time of true sunset. 

Daylight is also prolonged by the reflectio7i of the sun's 
rays (after sunset and before sunrise) from the small parti- 
cles of matter suspended in the atmosphere. This pro- 
duces a general though faint illumination of the atmos- 
phere, just as the light scattered from the floating particles 
of dust illuminated by a sunbeam let in through a crack 
in a shutter may brighten the whole of a darkened room. 

The sun's direct rays do not reach an observer on the 



TWILIGHT. 



173 



earth after the instant of sunset, since the solid body of 
the earth intercepts them. But the sun's direct rays 
illuminate the clouds and the suspended particles of the 
upper air, and are reflected downwards so as to produce a 
general illumination of the atmosphere. 

In the figure let A B CD he the earth and A an observer 
on its surface, to whom the sun S is just setting. A a is 
the horizon of A; Bb of Bj Cc of Cj Dd ot D. Let the 




Fig. 53. 



circle P QR represent the upper layer of the atmosphere. 
Between ABCD and PQR the air is filled with sus- 
pended particles which will reflect light. The lowest ray 
of the sun, SAM, just grazes the earth at A ; the higher 
rays /S^and SO strike the atmosphere above A and leave 
it at the points Q and R. Each of the lines S A P M, 
SQN, is bent from a straight course by refraction, but 
S R is not bent since it just touches the upper limits of 



174 ASTitONOMr. 

the atmosphere. The space MA BCD Bis the earth's 
shadow. An observer at A receives the (hist) direct rays 
fx'om the sun, and also has his skyilhiminated by the reflec- 
tion from all the particles lying in the space PQRT 
which is all above his horizon A a. 

An observer at B receives no direct rays from the sun. 
It is after sunset. Nor does he receive any light from all 
that portion of the atmosphere below A P M; but^the por- 
tion P Rx, which lies above his horizon B b, is lighted by 
the sun's rays, and rellects to B a portion of the incident 
rays. 

This tioil'ujJtt is strongest at R, and fades away gradu- 
ally toward P. 

To an observer at C the twilight is derived from the 
illumination of the portion PQz whicii lies above his 
horizon C c. 

To an observer at i) it is night. All of the illuminated 
atmosphere is below his horizon D d. 

The student should notice for himself the twilight arch 
which appears in the west after sunset. It is more marked 
in summer than in winter; in high latitudes than in low 
ones. There is no true night in England in midsummer, 
for example, the morning twilight beginning before the 
evening twilight has ended ; and in the torrid zone there 
is no perceptible twilight. 

Aberration and the Motion of Light. 

Besides refraction, there is another cause which prev^nts 
our seeing the celestial bodies exactly in the true direction 
,in which they lie from us; namely, the progressive mo- 
tion of light. We see objects only by the light which 
emanates from them and reaches our eyes, and we know 



REFRACTION AND ABERRATION OF LIGHT. 175 

that this light requires time to pass over the space which 
separates ns from the himinous object. After the ray of 
light once leaves the object, the latter may move away, or 
even be blotted out of existence, but the ray of light 
will continue on its course. Consequently when we look 
at a star, we do not see the star that now is, but the star 
that was several years ago. If it should be annihilated, we 
should still see it during the years which would be required 
for the last ray of light emitted by it to reach us. The 
velocity of light is so great that in all observations of ter- 
restrial objects our vision may be regarded as instantane- 
ous. But in celestial observations the time required for 
the light to reach us is quite appreciable and measurable. 

The discovery of the propagation of light is among the 
most remarkable of those made by modern science. The 
fact that light requires time to travel was first learned by 
the observations of the satellites of Jtqjiter. Owing to 
the great magnitude of this planet, it casts a much longer 
and larger shadow than our earth does, and its inner sat- 
ellite passes through this shadow and is eclipsed, at every 
revolution. These eclipses can be observed from the earth, 
the satellite vanishing from view as it enters the shadow, 
and reappearing when it leaves it again. The astronomers 
of the seventeenth century made a careful study of the mo- 
tions of these bodies. It was, however, necessary to con- 
struct tables by which the times of the eclipses could be pre- 
dicted. It was found by Roemer that these times depended 
oh the distance of Jupiter from the earth. If he made his 
tables agree with observations when the earth was nearest 
Jupiter f it was found that as the earth receded from Jupiter 
in its annual course around the sun, the eclipses were con- 
stantly seen later, until, when at its greatest distance, the 



176 ASTRONOMY. 

times appeared to be 22 minutes late. Roemer saw that it 
was in the highest degree improbable that the actual motions 
of the satellites should be affected with any such inequality; 
he therefore propounded the bold theory that it took time 
for light to come from Jupiter to the earth. The extreme 
differences in the times of the eclipse being 22 minutes, he 
assigned this as the time required for light to cross the 
orbit of the earth, and so concluded that it came from the 
sun to the earth in 11 minutes. This estimate was too 
great; the true time for this passage being about 8 minutes 
and 18 seconds. 

Discovery of Aberration. — This theory of Roemee was 
not fully accepted by his contemporaries. But in the year 
1729 the celebrated Bradley, afterward Astronomer Royal 
of England, discovered a phenomenon of an entirely dif- 
ferent character, which confirmed the theory. He was 
then engaged in making observations on the star y Dra- 
conis in order to determine its parallax. The effect of 
parallax would have been to make the declination of the 
star greatest in June and least in December, while in 
March and September the star would occupy an interme- 
diate or mean position. But the result was entirely dif- 
ferent. The declinations of June and December were the 
same, showing no effect of parallax; but instead of remain- 
ing constant the rest of the year, the declination was some 
40 seconds greater in September than in March, when the 
effect of parallax would be the same. This showed that 
the direction of the star appeared different, not according 
to the position of the earth in its orbit, but according to 
the direction of the earth's motion around the sun, the 
star being apparently displaced in this direction. 

To show how this is, let Ji5 be the optical axis of a 



UEFB ACTION AND ABERRATION OF LIGHT 17? 




telescope, and S a star from which emanates a ray moving 
in the true direction SAB'. Per- 
haps the student will have a clearer 
conception of the subject if he imag- 
ines AB to be a rod which an ob- 
server at B seeks to point at the star 
S. It is evident that he will point 
this rod in such a way that the ray 
of light shall run accurately along its 
length. Suppose now that the ob- 
server is moving from B toward B' 
with such a velocity that he moves fig. 54. 

from B to B' during the time required for a ray of light to 
move from A to B'. Suppose, also, that the ray of light 
SA reaches A at the same time that the end of his rod 
does. Then it is clear that while the rod is moving from 
the position ^Z^ to the position A'B', the ray of light 
will move from A to B', and will therefore run accurately 
along the length of the rod. For instance, if l is one third 
of the way from B to B', then the light, at the instant of 
the rod taking the position h a, will be one third of the way 
from A to B', and will therefore be accurately on the rod. 
Consequently, to the observer, the rod will appear to be 
pointed at the star. In reality, however, the pointing will 
not be in the true direction of the star, but will deviate 
from it by a certain angle depending upon the ratio of the 
velocity with which the observer is carried along to the 
velocity of light. This presupposes that the motion of the 
observer is at right angles to that of a ray of light. If 
this is not his direction, we must resolve his velocity into 
two components, one at right angles to the ray and one 
prallel to it, The latter will not affect the apparent di^ 



178 ASTRONOMY. 

rection of the star, which will therefore depend entirely 
upon the former. 

EiFects of Aberration. — The apparent displacement of 
the heavenly bodies thus produced is called the aberration 
of light. Its effect is to cause each of the fixed stars to 
ascribe an apparent annual oscillation in a very small orbit. 
The nature of the displacement may be conceived of in the 
following way: Suppose the earth at any moment, in the 
course of its annual revolution, to be moving toward a 
point of the celestial sphere, which we may call P. Then 
a star lying in the direction P or in the opposite direction 
will suffer no displacement whatever. A star lying in any 
other direction will be displaced in the direction of the 
point P by an angle depending upon its angular distance 
from P. At 90° from P the displacement will be a maxi- 
mum. 

Now, if the star lies hear the pole of the ecliptic, its di- 
rection will always be nearly at right angles to the direc^ 
tion in which the earth is moving. A little consideration 
will show that it will seem to describe a circle in conse- 
quence of aberration. If, however, it lies in the plane of 
the earth's orbit, then the various points toward which the 
earth moves in the course of the year all lying in the eclip- 
tic, and the star being in this same plane, the apparent 
motion will be an oscillation back and forth in this plane, 
and in all other positions the apparent motion will be in an 
ellipse more and more flattened as we approach the ecliptic. 
The maximum displacement of a star by aberration is 20'. 44. 

The connection between the velocity of light and the dis- 
tance of the sun is such that knowing one we can infer the 
other. Let us assume, for instance, that the time required 
for light to reach us from the siiji is 498 seconds, which 



BEFRACTION AND ABERRATION OF LIGHT. 179 

is probably accurate within a single second. Then know- 
ing the distance of the sun, we may obtain the velocity 
of light by dividing it by 498. But, on the other hand, 
if we can determine how many miles light moves in a 
second, we can thence infer the distance of the sun by 
multiplying it by the same factor. During the last cen- 
tury the distance of the sun was found to be certainly be- 
tween 90 and 100 millions of miles. It was therefore 
correctly concluded that the velocity of light was some- 
thing less than 200,000 miles per second, and probably 
between 180,000 and 200,000. This velocity has since 
been determined more exactly by the direct measurements 
at the surface of the earth already mentioned. 



CHAPTER XII. 
CHRONOLOGY. 

Astronomical Measures of Time. 

The intimate relation of astronomy to the daily life of 
mankind has arisen from its affording the only reliable and 
accurate measure of intervals of time. The fundamental 
units of time in all ages have been the day, the month, and 
the year, the first being measured by the revolution of the 
earth on its axis, the second, primitively, by that of the 
moon around the earth, and the third by that of the earth 
round the sun. 

Of the three units of time just mentioned, the most nat- 
ural and striking is the shortest; nan-iely, the day. It is 
so nearly uniform in length that the most refined astro- 
nomical observations of modern times have never certainly 
indicated any change. This uniformity, and its entire 
freedom from all ambiguity of meaning, have always made 
the day a common fundamental unit of astronomers. Ex- 
cept for the inconvenience of keeping count of the great 
naniber of days between remote epochs, no greater unit 
would ever have been necessary, and we might all date our 
letters by the number of days after Christ, or after any 
other fixed dat/C. 

The difficulty of remembering great numbers is such 
that a longer unit is absolutely necessary, even in keeping 
the reckoning of time for a single generation. Such a unit 



CHRONOLOGY. 181 

is the year. The regular changes of seasons in all extra- 
tropical latitudes renders this unit second only to the day 
in the prominence with which it must have struck the 
minds of primitive man. These changes are, however, so 
slow and ill-marked in their progress that it would have 
been scarcely possible to make an accurate determination 
of the length of the year from the observation of the sea- 
sons. Here astronomical observations came to the aid 
of our progenitors, and, before the beginnings of history, 
it was known that the alternation of seasons was due to 
the varying declination of the sun, as the latter seemed 
to perform its annual course among the stars in the 
**' oblique circle" or ecliptic. The seasons were also marked 
by the position of certain bright stars relatively to the sun; 
that is, by those stars rising or setting in the morning 
or evening twilight. Thus arose two methods of measur- 
ing the length of the year — the one by the time when the 
sun crossed the equinoxes or solstices, tlic other when it 
seemed to pass a certain point among the stars. As we 
have already explained, these years were sliglitly different, 
owing to the precession of the equinoxo?, tlie tirst or equi- 
noctial year being a little le.-s and the .-econd or sidereal 
year a little greater than 305:^ days. 

The number of days in a year is too great to admit of 
their bring easily remembered without any break; :in 
intermediate period is tlierefure necessary. Such a, pci'iod 
is measured by the revolution of the moon around the 
earth, or, more exactly, by the recurrence of new moon, 
which takes place, on the average, at the end of nearly 
29-^ days. The nearest round number to this is 30 days, 
and 12 periods of 30 days each only lack 5:^ days of being 
a year. It has therefore beeu common to consider a year 



182 ASTRONOMY. 

as made up of 12 months, the lack of exact correspondence 
being filled by various alterations of the length of the 
month or of the year, or by adding surplus days to each 
year. 

The true lengths of the day, the month, and the year 
having no common divisor, a difficulty arises in attempting 
to make months or days into years, or days into months, 
owing to the fractions which will always be left over. At 
the same time, some rule bearing on the subject is neces- 
sary in order that people may be able to remember the year, 
month, and day. Such rules are found by choosing some 
cycle ox period which is very nearly an exact number of 
two units, of months and of days for example, and by 
dividing this cycle up as evenly as joossible. 

Formation of Calendars. 

The months now or heretofore in use among the peoples of the 
gh)l)e may for the most p;irt be divided into two classes; 

(1) The hinar month pure and simple, ojr the mean interval be- 
tween successive new moons. 

(2) xVn approximation to the twelfth part of a year, without respect 
to the motion of tlie moon. 

The Lunar Month. — Tiie mean interval between consecutive new 
moons beii'.g nearly 291 da^'s, it was common in the use of the pure 
lunar month to have months of 29 and oO days jd'.ernitely. This 
supposed period, however, will fall short by a da}- in about 2^ years. 
This defect was remedied by introducing cycles containing rather more 
months of 30 than of 29 days, the small excess of long months being 
spread uniformly through the cycle. Thus the Greeks had a cycle 
of 235 months, of which 125 were full or long months, and 110 were 
short or deficient ones. We see that the length of this cycle ^vas 
6940 days (125 X 30 + 110 X 29), whereas the length of 235 true lunar 
months is 235 X 29.53088 = 6939.688 days. The cycle was therefore 
too long by less than one third of a day, and the error of count would 
amount to only one daj^ in more than 70 years. The Mohammedans, 
again, took a cycle of 360 months, which they divided into 169 short 
and 191 long ones. The length of this cycle was 10631 days, while 



mRONOLOOT. 183 

the true length of 360 lunar months is 10631.012 days. The count 
would therefore not be a day in error until the end of about 80 
cycles, or nearly 23 centuries. This month therefore follows the 
moon closely enough for all practical purposes. 

Months other than Lunar. — The complications of the system just 
described, and the consequent difficulty of making the calendar 
month represent the course of the moon, are so great that the pure 
lunar month was generally abandoned, except among people whose 
religion required irnportant ceremonies at the time of new moon. In 
such cases the year has been usually divided into 12 months of 
slightly different lengths. The ancient Egyptians, however, had 13 
months of 30 days each, to which they added 5 supplementary days 
at the close of each year. 

Kinds of Year. — As we find two different systems of months to 
have been used, so we may divide the calendar years into three 
classes, namely; 

(1) The lunar year, of 12 lunar months. 

(2) The solar year. 

(3) The combined luni-solar year. 

The Lunar Year. — We have already called attention to the fact that 
the time of recurrence of the year is not well marked except by 
astronomical phenomena which the casual observer would hardly 
remark. But the time of new moon, or of beginning of the month, 
is always well marked. Consequently it was very natural for people 
to begin by considering the year as made up of twelve lunations, the 
error of eleven days being unnoticeable in a single year unless care- 
ful astronomical observations were made. Even when this error was 
fully recognized, it might be considered better to use the regular 
year of 12 lunar months than to use one of an irregular or varying 
number of months. The Mohammedans use such a year to this day. 

The Solar Year. — In forming this year, the attempt to measure the 
year by revolutions of the moon is entirely abandoned, and its length 
is made to depend entirely on the change of the seasons. The solar 
year thus indicated is that most used in both ancient and modern 
times. Its length has been known to be nearly 365i days from the 
times of the earliest astronomers, and the system ^adopted in our cal- 
endar of having three years of 365 days each, followed by one of 366 
days, has been employed in China from the remotest historic times. 
This year of 365J days is now called by us the Julian Tear, after 
Julius C^sar, from whom we obtained it. 

The Metonic Cycle. — These considerations will enable us to under- 
stand the origin of our own calendar. We begin with the Metonic 
Cycle of the ancient Greeks, which still regulates some religious fes- 



184 ASTRONOMY. 

tivals, although it has disappeared from our civil reckoning of time. 
The necessity of employing lunar months caused the Greeks great 
difficulty in regulating their calendar so as to accord with their rules 
for religious feasts, until a solution of the problem was found by 
Meton, about 433 b.c. The discovery of Meton was that a period 
or cycle of 6940 days could be divided up into 235 lunar months, and 
also into 19 solar years. Of these months, 125 were to be of 30 days 
each and 110 of 29 days each, which would, in all, make up the re- 
quired 6940 days. To see how nearly this rule represents the actual 
motions of the sun and moon, we remark that: 

Days. Hours. Min. 

235 lunations require 6939 16 31 

19 Julian years require 6939 18 

19 true solar years require 6939 14 27 

We see that though the cycle of 6940 days is a few hours too 
long, yet if we take 235 true lunar months, we find their whole dura- 
tion to be a little less than 19 Julian years of 365|- days each, and a 
little more than 19 true solar years. 

The problem was to take these 235 months and divide them up 
into 19 years, of which 12 should have 12 months each and 7 
should have 13 months each. The long years, or those of 13 months, 
were probably those corresponding to tiie numbers 3, 5, 8, 11, 13, 16, 
and 19, while the first, second, fourth, sixth, .etc., were short years. 
In general, the months had 29 and 30 days alternately, but it was 
necessary to substitute a long month for a short one every two or 
three years, so that in the cycle there should be 125 long and 110 
short months. 

Golden Number. — This is simply the number of the year in the 
Metonic Cycle, and is said to owe its appellation to the enthusiasm 
of the Greeks over Meton's discovery, the authorities having ordered 
the division and numbering of the years in the new calendar to be 
inscribed on public monuments in letters of gold. The rule for find- 
ing the golden number is to divide the number of the year by 19 and 
add 1 to the remainder. From 1881 to 1899 it may be found by sim- 
ply subtracting 1880 from the year. It is employed in our church 
calendar for finding the time of Easter Sunday. 

The Julian Calendar. — The civil calendar now in use throughout 
Christendom had its origin among the Romans, and its foundation 
was laid by Julius C^sar. Before his time, Rome can hardly be 
said to have had a chronological system, the length of the year not 
being prescribed by any invariably rule, and being therefore changed 
from time to time to suit the caprice or to compass the ends of the 



OBBONOLOGf. 185 

rulers. Instances of this tampering disposition are familiar to the 
historical student. It is said, for instance, that the Gauls having to 
pay a certain monthly tiibute to the Romans, one of the governors 
ordered the year to be divided into 14 months, in order that the pay- 
days might recur more rapidly. A year was fixed at 365 days, with 
the addition of one day to every fourth year. The old Roman months 
were afterward adjusted to the Julian year in such a way as to give 
rise to the somewhat irregular arrangement of months which we now 
have. 

Old and New Styles. — The mean length of the Julian year is 365i 
days, about ll^^t Dili^utes greater than that of the true equinoctial 
year, wiiich measures the recurrence of the seasons. This difference 
is of little practical importance, as it only amounts to a week in a 
thousand years, and a change of this amount in that period is pro- 
ductive of no inconvenience. But, desirous to have the year as cor- 
rect as possible, two changes were introduced into the calendar by 
Pope Gregory XIII. with this object. They were as follows : 

(1) The day following October 4, 1583, was called the 15th instead 
of the 5th, thus advancing the count 10 days. 

(2) The closing year of each century, 1600, 1700, etc., instead of 
being always a leap-year, as in the Julian calendar, is such only 
when the number of the century is divisible by 4. Thus while 1600 
remained a leap-year, as before, 1700, 1800, and 1900 were to be 
common years. 

This change in the calendar w^as speedily adopted by all Catholic 
countries, and more slowly by Protestant ones, England holding out 
until 1752. In Russia it has never been adopted at all, the Julian 
calendar being still continued without change. The Russian reckon- 
ing is therefore 12 days behind ours, the ten days dropped in 1582 
being increased by the days dropped from the years 1700 and 1800 in 
the new reckoning. This modified calendar is called the Gregorian 
Calendar, or New Style, while the old system is called the Julian 
Calendar, or Old Style. 

It is to be remarked tbat the practice of commencing the year on 
January 1st was not universal until comparatively recent times. The 
most common times of commencing were, perhaps, March 1st and 
March 22d, the latter being the time of the vernal equinox. But 
January 1st gradually made its wa}'', and became universal after its 
adoption by England in 1752. 

Solar Cycle and Dominical Letter. — In our church calendars Janu- 
ary 1st is marked by the letter A, January 2d by B, and so on to G, 
when the seven letters begin over again, and are repeated through 
the year in the same order. Each letter there indicates the same day 



186 ASTRONOMY. 

of the week throughout each separate year, A indicating the day on 
which January 1st falls, B the day following, and so on. An excep- 
tion occurs in leap years, when February 29th and March 1st are 
marked by the same letter, so that a change occurs at the beginning 
of March. The letter corresponding to Sunday on this scheme is 
called the Dominical or Sunday letter, and when we once know 
what letter it is, all the Sundays of the year are indicated by that 
letter, and hence all the other days of the week by their letters. In 
leap-years there will be two Dominical letters, that for the last ten 
months of the year being the one next preceding the letter for 
January and February. In the Julian calendar the Dominical letter 
must always recur at the end of 28 years (besides three recurrences 
at unequal intervals in the mean time). This period is called the 
solar cycle, and determines the days of the week on which the days 
of the month fall during each year. 

Since any day of any year occurs one day later in the week than 
it did the year before, cr two days later when a 29th of February 
has intervened, the Dominical letters recur in the order G, F, E, D, 
C, B, A, G, etc. This may also be expressed by saying that any day 
of a past year occurred one day earlier in the week for every year 
that has elapsed, and, in addition, one day earlier for every 29th of 
February that has intervened. This fact will make it easy to calcu- 
late the day of the week on which any historical event happened 
from the day corresponding in any past or future year. Let us take 
the following example: 

On what day of the week was Washington born, the date being 
1732, February 22d, knowing that February 22d, 1879, fell on 
Saturday? The interval is 147 years: dividing by 4 we have a 
quotient of 36 and a remainder of 3, showing that, had every fourth 
year in the interval been a leap-year, there were either 36 or 37 leap- 
years. As a February 29th followed only a week after the date, the 
number must be 37;* but as 1800 was dropped from the list of leap- 
years, the number was really only 36. Then 147 + 36 = 183 days 
advanced in the week. Dividing by 7, because the same day of the 
week recurs after seven days, we find a remainder of 1. So 
February 22d, 1879, is one day further advanced than was Febru- 
ary 22d, 1733; so the former being Saturday, Washington was born 
on Friday. 

* Perhaps the most convenient way of deciding whether the remainder does 
or does not indicate an additional leap-year is to subtract it from the last date, 
and see whether a February 29th then intervenes. Subtracting 3 years from 
February 22d, 1879, we have February 22d 1876, and a 29th occurs between the 
twoldates, only a- week after the first. 



CHRONOLOGY. 187 



Division ot the Day. 

The division of the day into hours was, in ancient and mediaeval 
times, effected in a way very different from that which we practise. 
Artificial time-keepers not being in general use, the two funda- 
mental moments were sunrise and sunset, which marked the day as 
distinct from the night. The first subdivision of this interval was 
marked by the instant of noon, when tlie sun was on the meridian. 
The day was thus subdivided into two parts. The night was 
similarly divided by the times of rising and culmination of the 
various constellations. Euripides (480^07 B.C.) makes the chorus 
in Bhesus ask : 

" Chorus.— Whose is the guard? Who takes my turn? The first 
signs are setting, and the seven Pleiades are in the sky, and the Eagle 
glides midway through heaven. Awake! Why do you delay? Awake 
from your beds to watch! See ye not the brilliancy of the moon? 
Morn, morn indeed is approaching, and hither is one of the forerun- 
ning stars. " 

The interval between sunrise and sunset was divided into twelve 
equal parts called hours, and as this interval varied with the season, 
the length of the hour varied also. The night, whether long or 
short, was divided into hours of the same character, only when the 
night hours were long those of the day were short, and vice versa. 
These variable hours were called temporary hours. At the time of 
the equinoxes both the day and the night hours were of the same 
length with those we use; namely, the twenty-fourth part of the 
day ; these were therefore called equinoctial hours. 

Instead of commencing the civil day at midnight, as we do, it was 
customary to commence it at sunset. The Jewish Sabbath, for 
instance, commenced as soon as the sun set on Friday, and ended 
when it set on Saturday. This made a more distinctive division of 
the astronomical day than that which we employ, and led naturally 
to considering the day and the 7iig?U as two distinct periods, each to 
be divided into 12 hours. 

So long as temporary hours were used, the beginning of the day 
and the beginning of the night, or, as we should call it, six o'clock 
in the morning and six o'clock in the evening, were marked by the 
rising and setting of the sun; but when equinoctial houirs were 
introduced, neither sunrise nor sunset could be taken to count from, 
because both varied too much in the course of the year. It therefore 
became customary to count from noon, or the time at which the sun 
passed the meridian. The old habit of dividing the day and the 



1B8 AsmONOMY, 

night each into 12 parts was continued, the first 12 being reckoned 
from midnight to noon, and tlie second from noon to midnight. TI)e 
day was made to commence at midnight rather than at noon for 
obvious reasons of convenience, although noon was of course the 
point at which the time had to be determined. 

Equation of Time.— To any one who studied the annual motion of 
the sun, it must have been quite evident that the intervals between 
it.s successive passages over the meridian, or between one noon and 
the next, could not be the same throughout the year, because the 
apparent motion of the sun in right ascension is not constant. It 
will be remembered that the apparent revolution of the starry 
sphere, or, which is the same thing, the diurnal revolution of the 
earth upon its axis, may be regarded as absolutely constant for all 
practical purposes. This revolution is measured around in right 
ascension as explained in the opening chapter of this work. If the 
sun increased its right ascension by the same amount every day, it 
would pass the meridian 3"" 56*. later every day, as measured by 
sidereal time, and hence the intervals between successive passages 
would be equal. But the motion of the sun in right ascension is 
unequal from two causes: (1) the unequal motion of the earth in its 
annual revolution around it, arising from the eccentricity of the 
earth's orbit, and (2) the obliquity of the ecliptic. How the first 
cause produces an inequality is obvious. The mean motion is 3"" 56»; 
the actual motion varies from 3"' 48^ to 4'" 4^ 

The effect of the obliquity of the ecliptic is still greater. When 
the sun is near the equinox, the direction of its motion along the 
ecliptic makes an angle of 23^° with the parallels of declination. 
Since its motion in right ascension is measured along the parallel of 
declination, we see that it is less than the motion in longitude. The 
days are then 20 seconds shorter than they would be were there no 
obliquity. At the solstices the opposite effect is produced. Here 
the different meridians of right ascension are nearer together than 
they are at the equator; when the sun moves through one degree 
along the ecliptic, it changes its right ascension by l°-08; here, 
therefore, the days are about 19 seconds longer than they would be 
if the obliquity of the ecliptic were zero. 

We thus have to recognize two slightly different kinds of days: 
solar days and mean days. A solar day is the interval of time 
between two successive transits of the sun over the same meridian, 
while a mean day is the mean of all the solar days in a year. If we 
had two clocks, one going with perfect uniformity, but regulated 
so as to keep as near the sun as possible, and the other changing its 
ra-te so as to always follow the sun, the latter would gain or lose oij 



CHnoNOLOGT. 1^9 

the former by amounts sometimes rising to 22 seconds in a day. The 
accumulation of tliese variations through a period of several months 
would lead to such deviations that the sun-clock would be 14 minutes 
slower than the other during the first half of February, and 16 
minutes faster during the first week in November. The time-keepers 
formerly used were so imperfect that these inequalities in the solar 
day were nearly lost in the necessary irregularities of the rate of the 
clock. All clocks were therefore set by the sun as often as was 
found necessary or convenient. But during the last century it was 
found by astronomers that the use of units of time varying in this 
way led to much inconvenience; they therefore substituted mean 
time for solar or apparent time. 

Mean time is so measured that the hours and days shall always be 
of the same length, and shall, on the average, be as much behind the 
sun as ahead of it. We may imagine a fictitious or mean sun mov- 
ing along the equator at the rate of S"" 56* in right ascension every 
day. Mean time will then be measured by the passage of this 
fictitious sun across the meridian. Apparent time was used in 
ordinary life after it was given up by astronomers, because it was 
Very easy to set a clock from time to time as the sun passed a noon- 
mark. But when the clock was so far improved that it kept much 
better time than the sun did, it was found troublesome to keep put- 
ting it backward and forward so as to agree with the sun. Thus 
mean time was gradually introduced for all the purposes of ordinary 
life. 

The common household almanac should give the equation of time, 
or the mean time at which the sun passes the meridian, on each day 
of the year. Then, if any one wishes to set his clock, he knows the 
moment when the sun passes the meridian, or when it is at some noon- 
mark, and sets his time-piece accordingly. For all purposes where 
accurate time is required, recourse must be had to astronomical 
observation. It is now customary to send time-signals every day at 
noon, or some other hour agreed upon, from observatories along the 
principal lines of telegraph. Thus at the present time the moment 
of Washington noon is signalled to New York, and over the principal 
lines of railway to the South and West. Each person within reach 
of a telegraph-oflice can then determine his local time by correcting 
these signals for the difference of longitude. 



PART 11. 

THE SOLAR SYSTEM IN DETAIL. 



CHAPTER I. 

STRUCTURE OF THE SOLAR SYSTEM. 

The solar system consists of tlie sun as a central body, 
around which revolve the major and minor planets, with 
their satellites, a few periodic comets, and an unknown 
number of meteor swarms. These are permanent members 
of the system. At times other comets appear, and move 
usually in parabolas through the system, around the sun, 
and away from it into space again, thus visiting the system 
without being permanent members of it. 

The bodies of the system may be classified as follows : 

1. The central body — tlie Sun. 

2. The four inner planets — Mercury, Venus, the Earth, Mars. 

3. A group of small planets, sometimes called Asteroids, revolving 
outside of the orbit of Mars. 

4. A group of four outer planets — Jupiter, Saturn, Uranus, and 
Neptune. 

5. The satellites, or secondary bodies, revolving about the planets, 
their primaries. 

6. A number of comets and meteor swarms revolving in very 
eccentric orbits about the sun. 

The eight planets of Groups 2 and 4 are sometimes classed to- 
gether as the major planets, to distinguish them from the two hun- 
dred or more minor planets of Group 3. The formal definitions of 
the various classes, laid down by Sir William Herschel in 1802, are 
worthy of repetition : 



STRUCTURE OF THE SOLAR SYSTEM. 



191 



Planets are celestial bodies of a certain very considerable size. 
They move in not very eccentric ellipses about the sun. The planes 
of their orbits do not deviate many degrees from the plane of the 
earth's orbit. Their motion about the sun is direct (from west to 
east). They may have satellites or rings. They have atmospheres of 




Fig. 55.— Relative Surfaces of the Planets. 



considerable extent, which, however, bear hardly any sensible pro- 
portion to their diameters. Their orbits are at certain considerable 
distances from each other. 

Asteroids, now more generally known as small or minor planets, are 
celestial bodies which move about the sun in orbits, either of little ov 



192 



ASTRONOMY. 



of considerable eccentricity, the planes of which orbits may be in- 
clined to the ecliptic at any angle whatsoever. They may or may 
not have considerable atmospheres. 

Comets are celestial bodies, generally of a very small mass, though 
how far this may be limited is yet unknown. They move in very 




Fig. 56. — Apparent Magnitudes of the Sun as seen from Different Planets. 



eccentric ellipses or in parabolic arcs about the f-un. The planes of 
their motion admit of the greatest variety in their situation. The 
direction of their motion is also totally undetermined. They have 
atmospheres of very great extent, which sIiqw themselves in various 
forms as tails, coma, haziness, etc. 



STRUCTURE OF THE SOLAR SYSTEM. 



193 



Eelative Surfaces of the Planets. — The comparative surfaces of the 
major planets, as they would appear to an observer situated at an 
equal distance from all of them, is given in the figure on page 191. 

The relative apparent magnitudes of the sun, as seen from the 
various planets, is shown in the figure on page 192. 

Fld'a and Mnemosyne are two of the asteroids. 

A curious relation between the distances of the planets, known as 
Bode's law, deserves mention. If to the numbers 
0, 3, 6, 13. 24, 48, 96, 192, 384, 
each of which (the second excepted) is twice the pi-eceding, we add 
4, we obtain the series 

4, 7, 10, 16, 28, 52, 100, 196, 388. 

These last numbers represent approximately the distances of the 
planets from the sun (except for Neptune, which was not discovered 
when the so-called law was announced). 

This is shown in the following table : 



Planets. 



Mercury 
Venus. . 
Earth. . . 

Mars 

[Ceres] . , 
Jupiter. , 
Saturn. . 
Uranus. , 
Neptune 



Actual 
Distance. 



3.9 

7-2 
10-0 
15-2 
27-7 
52-0 
95-4 
191-8 
300-4 



Bode's Law. 



4-0 

7-0 

10-0 

16-0 

28-0 

52-0 

100-0 

:96.0 

388 



It will be observed that Neptune does not fall within this ingenious 
scheme. Ceres is one of the minor planets. 

The relative brightness of the sun and the various planets has been 
measured by Zollner, and the results are given below. The column 
per cent &\\o^'si\\Q percentage of error indicated in the separate re- 
sults: 



Sun and 



Moon 

Mars 

Jupiter 

Saturn (ball alone) 

Uranus 

Neptune 



Ratio : 1 to 


Percent, of Error: 


618.000 


1-6 


6,994.000,000 


5-8 


5.472.000,000 


5-7 


130,980,000,000 


5-0 


8,486.000.000,000 


6-0 


79,620,000,000,000 


5.5 



194 



ASTRONOMY. 



The differences in the density, size, mass, and distance of the 
several planets, and in the amount of solar light and heat which they 
receive, are immense. The distance of Neptune is eighty times that 
of Mercury, and it receives only -^^^-^ as much light and heat from the 
sun. The density of the earth is about six times that of water, while 
Saturn's mean density is less than that of water. 

The mass of the sun is far greater than that of any single planet 
in the system, or indeed than the combined mass of all of them. In 
general, it is a remarkable fact that the mass of any given planet ex- 
ceeds the sum of the masses of all the planets of less mass than itself. 
This is shown in the following table, where the masses of the planets 
are taken as fractions of the sun's mass, which we here express as 
1,000,000,000: 



b 

•1 

200 




to 

1 


5 
1 


g 


1 


3 

1 


1 

3 
1-5 


3 


Planets. 


324 


2,353 


3,060 


44,250 


51,600 


285,580 


954,305 


1,000,000,000 


Masses. 



The total mass of the small planets, like their number, is unknown, 
but it is probably less than one thousandth that of our earth, and 
would hardly increase the sum-total of the above masses of the solar 
system by more than one or two units. The sun's mass is thus over 
700 times that of all the other bodies, and hence the fact of its cen- 
tral position in the solar system is explained. In fact, the centre of 
grnvify of the whole solar system is very little outside the body of the 
sun, and will be inside of it when Jupiter and Saturn are in opposite 
directions from it. 

Planetary Aspects. — The motions of the planets about the sun have 
been explained in Chapter V. From what is there said it appears 
that the best time to see one of the outer planets will be when it is 
in opposition; that is, when its geocentric longitude or its right as- 
cension differs 180° or la** from that of the sun. At such a time the 
planet will rise at sunset and culminate at midnight. During the 
three months following opposition the planet will rise from three to 
six minutes earlier every day, so that, knowing when a planet is in 
opposition, it is easy to find it at any other time. For example, a 
month after opposition the planet will be two or three hours high 
about sunset, and will culminate about nine or ten o'clock. Of 
course the inner planets never come into opposition, and hence are 
best seen about the times of their greatest elongations. 



8TBUGTURE OF THE SOLAR SYSTEM. 



196 



Dimensions of the Solar System. — The figure gives a rough plan of 
part of the solar system as it would appear to a spectator immediately 
above or below the plane of the ecliptic. It is drawn approximately 
to scale, the mean distance of the earth (= 1) being half an inch. 
The mean distance of Saturn would be 4-77 inches, of Uranus 9-59 




Fio. 57. 

inches, of Neptune 15 '03 inches. On the same scale the distance of 
the 72ea?Tsi fixed star would be 103,133 inches, or over one and one half 
miles. 
The arrangement of the planets and satellites 'm, then — 



The Inner Group. 
Mercury. 
Venus. 

Earth and Moon. 
"^ars and 2 moons. 



Asteroids. 

200 minor planets, 

and probably 

many more. 



The Outer Group. 
( Jupiter and 4 moons. 
' Saturn and 8 moons. 

Uranus and 4 moons. 

Neptupe and 1 moon. 



196 ASTRONOMY. 

To avoid repetitions, the elements of the major planets and other 
data are collected into the two following tables, to which reference 
should be made by the student. The units in terms of which the vari- 
ous quantities are given are those familiar to us, as miles, days, etc., 
yet some of the distances, etc., are so immensely greater than any 
known to our daily experience that we must have recourse to illus- 
trations to obtain any idea of them at all. For example, the dis- 
tance of the sun is said to be 92| million jniles. Jt is of importance 
that some idea should be had of this distance, as it is the unit, in 
terms of which not only the distances in the solar system are ex- 
pressed, but which serves as a basis for measures in the stellar uni- 
verse. Thus when we say that tlie distance of the nearest star is over 
200,000 times the mean distance of the sun, it becomes necessary to see 
if some conception can be obtained of one factor in tliis. Of tlie ab- 
stract number, 92,500,000. we have no conception. It is far too 
great for us to have counted. We have never taken in at one view 
even a million similar discrete objects. The largest tree has less 
than 500,000 leaves. To count from 1 to 200 requires, Avith very 
rapid counting, 60 seconds. Suppose this kept up for a day witliout 
intermission ; at the end we should have counted 288,000, which is 
about gl^ of 92,500,000. Hence over 10 montlis' uninterrupted 
counting by night and day would be required simply to enumerate 
the nximher, and long before the expiration of the task all idea of it 
would have vanished We may take other and perhaps more strik- 
ing examples. We know, for instance, that the time of the fastest 
express-trains between New York and Chicago, which average 40 
miles per hour, is about a day. Suppose such a train to start for the 
sun and to continue running at this rapid rate. It would take 363 
years for the journey. Three hundred and sixty-three years ago there 
was not a European ?ettlement in America. 

A cannon-ball moving continuously across the intervening space 
at its highest speed would require about nine years to reach the sun. 
The report of the cannon, if it could be conve3'ed to the sun with 
the velocity of sound in air, would arrive there five years after the 
projectile. Such a distance is entirely inconceivable, and yet it is 
only a small fraction of those with w-hich astronomy has to deal, even 
in our own system. The distance of Neptune is 30 times as great. 

If we examine the dimensions of the various orbs, we meet almost 
equally inconceivable numbers, The diarneter of the sun is 860.000 
miles; its radius is but 480,000, and yet this is nearly twice the mean 
distance of the moon from the earth. Try to conceive, ip looking at 
the moon in a clear sky, that if the centre of the syin could be placed 
1^1 the ceiitfe of \]x^ ^9^x% tti§ moPR ^'9^1(i be f^p ^ithift tlie JiWfl'a 



STRUCTURE OF THE SOLAR SYSTEM. 197 

surface. Or again, conceive of the force of gravity at the surface of 
the various bodies of the system. At the sun it is nearly 28 times 
that known to us. A pendulum beating seconds here would, if 
transported to the sun, vibrate with a motion more rapid than that 
of a watch -balance. The muscles af the strongest man would not 
support him erect on the surface of the sun : even lying down he 
would crush himself to death under his own weight of two tons. 
We may by these illustrations get some rough idea of the meaning of 
the numbers in these tables, and of the incapability of our limited 
ideas to comprehend the true dimensions of even the solar system. 



198 



ASTRONOMY. 




JSmWTtlMB OF THE SOLAU SYSTEM. 



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CHAPTER 11. 

THE SUN. 

General Summary. 

To enable the nature of the phenomena of the snn to be 
clearly understood, we preface our account of its physical 
constitution by a brief summary of its main features. 

Photosphere. — To the simple yision the sun presents the 
aspect of a brilliant sphere. The yisible shining surface 
of this sphere is called the photosphere, to distinguish it 
from the body of the sun as a whole. The apparently flat 
surface presented by a view of the photosphere is called the 
sun's disk. 

Spots. — When the photosphere is examined with a tele- 
scope, small dark patches of varied and irregular outline 
are frequently found upon it. These are called the solar 
spots. 

Rotation. — When the spots are observed from day to 
day, they are found to move over the sun's disk from east to 
west in such a way as to show that the sun rotates on its 
axis in a period of 25 or 26 days. The sun, therefore, has 
axisy poles, and equator, like the earth, the axis being the 
line around which it rotates. 

Faculae.— Groups of minute specks brighter than the 
general surface of the sun are often seen in the neighbor- 
hood of spots or elsewhere. They are cdXltdi facul(B. 



Ghromosphere, or Sierra. — ^The solar photosphere is cov- 
ered by a layer of glowing vapors and gases of very irregu- 
lar depth. At the bottom lie the vapors of many metals, 
iron, etc., volatilized by the fervent heat which reigns 
there, while the upper portions are composed principally 
of hydrogen gas. This vaporous atmosphere is commonly 
called the chromosphere^ sometimes the sierra. It is en- 
tirely invisible to direct vision, whether with the telescope 
or naked eye, except for a few seconds about the beginning 
or end of a total eclipse, but it may be seen on any clear 
day through the spectroscope. 

Prominences, Protuberances, or Red Flames. — The gases 
of the chromosphere are frequently thrown up in irregular 
masses to vast heights above the photosphere, it may be 
50,000, 100,000, or even 200,000 kilometres. Like the 
chromosphere, these masses have to be studied with the 
spectroscope, and can never be directly seen except when 
the sunlight is cut off by the intervention of the moon 
during a total eclipse. They are then seen as rose-colored 
flames, or piles of bright red clouds of irregular and fantas- 
tic shapes. \ 

Corona.— During total eclipses the sun is seen to be en- 
veloped by a mass of soft white light, much fainter than 
the chromosphere, and extending out on all sides far be- 
yond the highest prominences. It is brightest around the 
edge of the sun, and fades off toward its outer boundary, 
by insensible gradations. This halo of light is called the 
corona, and is a very striking object during a total eclipse. 

The Photosphere. 

Aspect and Stracture of the Photosphere. — The disk of the sim is cir« 
cular in shape, no matter what side of the sun's globe is turned to- 



20^ 



ASTRONOMY. 



ward us, whence it follows that the sun itself is a sphere. The aspect 
of the disk, when viewed with the naked eye, or with a telescope of 
low power, is that of a uniform bright, shining surface, hence called 
the photosphere. With a telescope of higher power the photosphere 
is seen to be diversified with groups of spots, and under good con- 




Fia. 58.— Reticulated Arrangement of the Sun's Photosphere. 
(From a photograph.) 



ditions the whole mass has a mottled or curdled appearance. This 
mottling is caused by the presence of cloud-like forms, whose out- 
lines though faint are yet distinguishable. The background is also 
covered with small white dots or forms still smaller than the clouds* 



THE BVN. 203 

These are the " rice-grains," so called. The clouds themselves are 
composed of small, intensely bright bodies, irregularly distributed, 
of tolerably definite shapes, which seem to be suspended in or super- 
posed on a darker medium or background. The spaces between the 
bright dots vary in diameter from 2" to 4" (about 1400 to 2800 kilo- 
metres). The rice-grains themselves have been seen to be composed 
of smaller granules, sometimes not more than 0".3 (135 miles) in 
diameter, clustered together. Thus there have been seen at least 
three orders of aggregation in the brighter parts of the photosphere: 
the larger cloud-like forms; the rice-grains; and, smallest of all, the 
granules. 

Light and Heat from the Photosphere. — The pliotospTiere 
is not equally bright all over the apparent disk. This is at 
once evident to the eye in observing the sun with a tele- 
scope. The centre of the disk is most brilliant, and the 
edges or 117111)8 are shaded off so as to forcibly suggest the 
idea of an absorptive atmosphere, which, in fact, is the 
cause of this appearance. 

Such absorption occurs not only for the rays by which 
we see the sun, the so-called visual rays, but for those 
which have the most powerful effect in decomposing the 
salts of silver, the so-called chemical rays, by which the 
ordinary photograph is taken. 

The amount of heat received from different portions of 
the sun's disk is also variable, according to the part of the 
apparent disk examined. This is what we should expect. 
That is, if the intensity of any one of these radiations (as 
felt at the earth) varies from centre to circumference, that 
of every other should also vary, since they are all modifi- 
cations of the same primitive motion of the sun's con- 
stituent particles. But the constitution of the sun's at- 
mosphere is such that the law of variation for the three 
classes is different. The intensity of the radiation in the 
sun itself and inside of the absorptive atmosphere is prob- 



^04 A&TBONOMt. 

ably nearly constant. The ray wliich. leaves the centre 
of the sun's disk in passing to the eartli traverses the 
smallest possible thickness of the solar atmosphere, while 
the rays from points of the sun's body which appear to us 
near the limbs pass, on the contrary, through the maxi- 
mum thickness of atmosphere, and are thus longest sub- 
jected to its absorptive action. 

This is plainly a rational explanation, since the part of 
the sun which is seen by us as the limb varies with the 
position of the earth in its orbit and with the position of 
the sun's surface in its rotation, and has itself no physical 
peculiarity. The various absorptions of different classes 
of rays correspond to this supposition, the more refrangi- 
ble rays, violet and blue, suffering most absorption, as they 
must do, being composed of waves of shorter wave-length. 

Amount of Heat Emitted by the Sun. — Owing to the 
absorption of the solar atmosphere, it follows that we re- 
ceive only a portion — perhaps a very small portion — of 
the rays emitted by the sun's photosphere. 

If the sun had no absorptive atmosphere, it would seem 
to us hotter, brighter, and more blue in color. 

Exact notions as to how great this absorption is are hard 
to gain, but it maybe said roughly that the best authorities 
agree that although it is quite possible that the sun's at- 
mosphere absorbs half the emitted rays, it probably does 
not absorb four fifths of them. 

The amount of this absorption is a practical question to 
us on the earth. So long as the central body of the sun 
continues to emit the same quantity of rays, it is plain that 
the thickness of the solar atmosphere determines the num- 
ber of such rays reaching the earth. If in former times 
this atmosphere was much thicker, then less heat would 



THE SUM, 205 

have reached the earth. Glacial epochs may be explained 
in this way. If the central body of the sun has likewise 
had different emissive poAvers at different times, this again 
would produce a yariation in the temperature of the earth. 

Amount of Heat Radiated. — There is at present nowa}^ of deteimin- 
ing accurately either the absolute amount of heat emitted from the 
central body or the amount of this heat stopped by the solar atmos- 
phere itself. All that can be done is to measure (and that only 
rouglily) the amount of heat really received by the earth, without 
attempting to define accurately the circumstances which this radiation 
has undergone before reaching the earth. 

PouiLLET has experimented upon this question, making allowance 
for the time that the sun is below the horizon of any place, and for 
the fact that the solar rays do not in general strike perpendicularly 
but obliquely upon any given part of the earth's surface. His con- 
clusions may be stated as follows : if our own atmosphere were re- 
moved, the solar rays would have energy enough to melt a layer of 
ice 9 centimetres thick over the whole earth daily, or a layer of about 
32 metres thick in a year. 

This action is constantly at work over the whole of the sun's sur- 
face. To produce a similar effect by the combustion of coal would 
require that a layer of coal 5 metres thick spread all over the sun 
should be consumed every hour. This is equivalent to a continuous 
evolution of 10,000 horse-power on every square foot of the sun's 
surface. If the sun were of solid coal and produced its own heat by 
combustion, it would burn out in 6000 years. 

Of this enormous outflow of heat the earth receives only 
•g^ooo^ooo o o- ^^ have expressed the power of even this small frac- 
tion' of the sun's heat in terms of the ice it would melt daily. If we 
compute how much coal it would require to melt the same amount, 
and then further calculate how much work this coal would do, we 
shall find that the sun sends to the earth an amount of heat which is 
equivalent to one horse-power continuously acting for every 30 
square feet of the earth's surface. Most of this is expended in main- 
taining the earth's temperature ; but a small portion, about ydW, is 
stored away by animals and vegetables, and this slight fraction is 
the source upon which the human race depends. If this were with- 
drawn the race would perish. 

Of the total amount of hont radiated by the sun the earth receives 
but an insignificant share. The sun is capable of heating the entire 
surface of a sohere whose radius is the earth's mean distance to the 



206 ASTRONOMY. 

same degree that the earth is now heated. The surface of such a 
sphere is 3,170,000,000 times greater thau tlie angular dimensions of 
the eartli as seen from the sun, and hence the earth receives less than 
one two-billionth part of the sohir radiation. The rest of the solar 
rays are, so far as we know, lost in space. 

Solar Temperature. — From the amount of heat actually radiated by 
the sun, attempts have been made to determine the actual tempera- 
ture of the solar surface. The estimates reached by various authori- 
ties differ widely, as the laws which govern the absorption within 
the solar envelope are almost unknown. Some such law of absorp- 
tion has to be supposed in any such investigation, and the estimates 
have differed widely according to the adapted law. 

Secchi estimates this temperature at about 6,100,000° C. Other 
estimates are far lower, but, according to all sound philosophy, the 
temperature must far exceed any terrestrial temperature. There can 
be no doubt that if the temperature of the earth's surface were sud- 
denly raised to that of the sun, no single chemical element would re- 
main in its present condition. The most refractory materials would 
be at once volatilized. 

We may concentrate the heat received upon several square feet 
(the surface of a huge burning-lens or mirror, for instance), examine 
its effects at the focus, and, making allowance for the condensation 
by the leas, see what is the minimum possible temperature of the 
sun. The temperature at the focus of the lens cannot be higher than 
that of the source of heat in the sun ; we can only concentrate the 
heat received on the surface of the lens to one point and examine its 
effects. If a lens three feet in diameter be used, the most refractory 
materials, as fire-clay, platinum, the diamond, are at once melted or 
volatilized. The effect of the lens is plainly the same as if the earth 
were brought closer to the sun, in the ratio of the diameter of the 
focal image to that of the lens. In the case of the lens of thiee feet, 
allowing for the absorption, etc., this distance is yet greater than 
that of the moon from the earth, so that it appears that any comet or 
planet so close as this to the sun, if composed of materials similar to 
those in the earth, must be vaporized. 

Sun-spots and FACTJL.a:. 

Avery cursory examination of the sun's disk with a small tele- 
scope will generally show one or more dark spots upon the photo- 
sphere. These are of various sizes, from minute black dots 1" or 2" 
in diameter (1000 kilometres or less) to large spots several minutes 
of arc in extent. 



THE SUK 



207 



Solar spots generally have a dark central nucleus or umbra, sur- 
rounded by a border or penumbra of grayish tint, intermediate in 
shade between the central blackness and the bright photosphere. 
By increasing the power of the telescope, the spots are seen to be of 
very complex forms. The umbra is often extremely irregular in 
shape, and is sometimes crossed by bridges or ligaments of shining 
matter. The penumbra is composed of filaments of brighter and 
darker light, which are arranged in striae. The general aspect of a 
spot under considerable magnifying power is shown in Fig. 59. 

The first printed account of solar spots was given by Fabritius in 
1611, and Galileo iu the same year (May, 1611) also described them. 




Fig. 59.— Umbra and Penumbra of Sun-spot. 



Galileo's observations show^ed them to belong to the sun itself, and 
to move uniformly across the solar disk from east to west. A spot 
just visible at the east limb of the sun on any one day travelled slow- 
ly across the disk for 12 or 14 days, when it reached the west limb, 
behind which it disappeared. After about the same period, it reap- 
pears at the eastern limb, unless, as is often the case, it has in the 
mean time vanished. 

The spots are not permanent in their nature, but are formed some- 
where on the sun, and disappear after lasting a few days, weeks, or 
months. But so long as they last they move regularly from east to 
west on the suu's apparent disk, making one complete rotation i^ 



208 ASTRONOMY. 

about 25 days. This period of 25 days is therefore approximately 
tlie rotation period of the sun itself. 

Spotted Region. — It is found that the spots are chiefly confined to 
two zones, one in each hemisphere, extending from about 10° to 35" 
or 40° of heliographic latitude. In the polar region spots are 
scarcely ever seen, and on the solar equator they are much more rare 
than in latitudes 10° north or south. Connected with the spots, but 
lying on or above the solar surface, are faculce, mottliugs of light 
brighter than the general surface of the sun. 




Fig. 60.— Photograph of the Sun. 

Solar Axis and Equator.— The spots must revolve with the surface 
of the sun about his axis, and tiie directions of their motions must be 
approximately parallel to his equator. Fig. 61 shows the appear- 
ances as actually observed, the dotted lines representing the apparent 
paths of the spots across the sun's disk at different times of the year. 
In June and December these paths, to an observer on the earth, seem 
to be right lines, and hence at these times the observer must be in the 
plane of the solar equator. At other times the paths are ellipses, and 
in March and September the planes of these ellipses are most oblique, 
slj«wing the spectator to be then furthest from the plane of the solar 
equator. The inclination of the solar equator to the ecliptic is about 
7° 9', and the axis of rotation is of course perpendicul^v to it, 



THE mK. 209 

Nature of the Spots. — The sun-spots are really depres 
sions in the photosphere, as was first pointed out by A:n"- 
DREW Wilson of Glasgow in 1774. When a spot is seen at 
the edge of the disk, it appears as a notch in the limb, and is 



Fig, 61. — Apparent Path of Solar Spot at Different Seasons. 

elliptical in shape. As the rotation carries it further and 
further on to the disk, it becomes more and more nearly 
circular in shape, and after passing the centre of the disk 
the appearances take place in reverse order. 

These observations were explained by Wilson, and more fully by 
Sir WjLWAM JIerschel, by supposing the suii to consist of an iur 



210 



ASTRONOMY. 



terior dark cool mass, surrounded by two layers of clouds. The 
outer layer, which forms the visible photosphere, was supposed ex- 
tremely brilliant. The inner layer, which could not be seen except 
when a cavity existed in the photosphere, was supposed to be dark. 
The appearance of the edges of a spot, which has been described as 
the penumbra, was supposed to arise from those dark clouds. Tlie 
spots themselves are, according to this view, nothing but openings 
through both of the atmospheres, the nucleus of the spot being simply 
the black surface of the inner sphere of the sun itself. 
This theory, Fig. 63, accounts for the facts as they were known 





Fig. 62.— Appearance of a Spot near the Limb and near the 
Centre op the Sun. 



to Herschel. But when it is confronted with the questions of the 
cause of the sun's heat and of the method by which this heat has 
been maintained constant in amount for centuries, it breaks down 
completely. The conclusions of Wilson and Herschel, that the 
spots are depressions in the sun's surface, are undoubted. But the 
existence of a cool central and solid nucleus to the sun is now 
known to be impossible. The apparently black centres of the spots 
are so mostly by contrast. If they were seen against a perfectly 
black background, they would appear very bright, as has been 
proved by photo^netric measures. And a cool solid nucleus beneatl^ 



THE SXIN. 2H 

such an atmosphere as Herschel supposed would soon become gas- 
eous by the couduction and radiation of the heat of the photosphere. 
The supply of solar heat, which has been very nearly constant dur- 
ing the historic period, in a sun so constituted would have sensibly 
diminished iu a few hundred years. For these and other reasons 
the hypothesis of Herschel must be modified, save as to the fact 
that the spots are really cavities in the photosphere. 

Number and Periodicity of Solar Spots. — The number of 
solar spots which come into view varies from year to year. 
Although at first sight this miglit seem to be what we call 
a purely accidental circumstance, like the occurrence of 
cloudy and clear years on the earth, observations of sun- 
spots establish the fact that this number xsivies periodically. 

The periodicity of the spots will appear from the following sum- 
mary: 

From 1828 to 1831 the sun was without spots on only 1 day. 

In 1833 " " " 139 days. 

From 1836 to 1840 " " " 3 " 

In 1843 " " " 147 " 

From 1847 to 1851 " " " 2 " 

In 1856 " " " 193 " 

From 1858 to 1861 '' " " no day. 

In 1867 '• " " 195 days. 

Every 11 years there is a minimum number of spots, and about 5 
years after each minimum there is a maximum. If, instead of mere- 
ly counting the number of spots, measurements are made on solar 
photographs of the extent of spotted area, the period comes out with 
greater distinctness. This periodicity of the area of the solar spots 
appears to be connected with magnetic phenomena on the earth's 
surface, and with the number of auroras visible. It has been sup- 
posed to be connected also with variations of temperature, of ram- 
fall, and with other meteorological phenomena such as the monsoons 
of the Indian Ocean, etc. The cause of this periodicity is as yet un- 
known. It probably lies withm the sun itself, and is similar to the 
cause of the periodic action of a geyser. As the periodic variations 
of the spots correspond to variations of the magnetic needle on the 
earth, it appears that there is a connection of an unknown nature 
between the sun and the earth. 



212 A8TB0N0MY. 



The Sun's Chkomosphere and Corona. 

Phenomena of Total Eclipses. — Tlie beginning of a total solar 
eclipse is marked simply by tlie small black notch made in the 
luminous disk of the sun by the advancing edge or limb of the 
moon. This always occurs on the western half of the sun, as the 
moon moves from west to east in its orbit. An hour or more must 
elapse before the moon has advanced sufficiently far in its orbit to 
cover the sun's disk. During this time the disk of the sun is gradu- 
ally hidden until it becomes a thin crescent. 

The actual amount of the sun's light may be diminished to two 
thirds or three fourths of its ordinary amount without its being 
strikingly perceptible to the eye. What is first noticed is the change 
which takes place in the color of the surrounding landscape, which 
begins to wear a ruddy aspect. This grows more and more pro- 
nounced, and gives to the adjacent country that weird effect which 
lends so much to the impressiveness of a total eclipse. The reason 
for the change of color is simple. We have already said that the 
sun's atmosphere absorbs a large proportion of the bluer ra3^«!, and as 
this absorption is dependent on the thickness of the solar atmosphere 
through which the rays must pass, it, is plain that just before the sun 
is totally covered the rays by which we see it will be redder than 
ordinary sunlight, as they are those which come from points near 
the sun's limb, where they have to pass through the greatest thick- 
ness of the sun's atmosphere. 

The color of the light becoines more and more lurid up to the mo- 
ment when the sun has nearly disappeared. If the spectator is upon 
the top of a high mountain, he can then begin to see the moon's 
shadow rushing toward him at the rate of a kilometre in about a 
second. Just as thp shadow reaches him there is a sudden increase 
of darkness; the brighter stars begin to shine in the dark lurid sky, 
the thin crescent of the sun breaks up intq small points or dots of 
light, which suddenly disappear, and the moon itself, an intensely 
black ball, appears to hang isolated in the heavens. 

An instant afterward the corona is seen surrounding the black 
disk of the moon with a soft effulgence quite different from any 
other light known to us. Near the moon's limb it is intensely bright, 
and to the naked eye uniform in structure; 5' or 10' from the limb 
this inner corona has a boundary more or less defined, and from this 
extend streamers and wings of fainter and more nebulous light. 
These are of various shapes, sizes, and brilliancy. No two ^o\qx 
eclipses yet qbserve4 haye bqen f^Ul^e jn tl<is respect, 



THE SUN. 213 

These appearances, though changeable, do not change in the time 
the moon's shadow requires to pass from Vancouver's Island to 
Texas, for example, which is some fifty minutes. 

Superposed upon these wings may be seen (sometimes with the 
naked eye) the red flames or protuberances whicli were first discov- 
ered during a solar eclipse. These need not be more closely de- 
scribed here, as they can now be studied at any time by aid of the 
spectroscope. 

The total phase lasts for a few minutes (never more than six or 
seven), and during this time, as the eye becomes more and more 
accustomed to the faint light, the outer corona is seen to stretch 
further and further away from the sun's linvb. At the eclipse of 1878, 
July 29th, it was seen to extend more than 6° (about 9,000,000 miles) 
from the sun's limb. Just before the end of the total phase there is 
a sudden increase of the brightness of the sky, due to the increased 
illumination of the earth's atmosphere near the observer, and in a 
moment more the sun's rays are again visible, seemingly as bright as 
ever. From the end of totality till the last contact thy phenomena 
of the first half of the eclipse are repeated in inverse order. 

Telescopic Aspect of the Corona. — Such are the appearances to the 
naked eye. The corona, as seen through a telescope, is, however, 
of a very complicated structure. The inner corona is usually com- 
posed of bright striie or filaments separated by darker bands, and 
some of these latter are sometimes seen to be almost totally black. 
The appearances are extremely irregular, but they are often as if the 
inner corona were made up of brushes of light on a darker back- 
ground. 

The corona and red prominences are solar appendages. It was 
formerly doubtful whether the corona was an atmosphere belonging 
to the sun or to the moon. At the eclipse of 1860 it was proved by 
measurements that the red prominences belonged to the sun and not 
to the moon, since the moon gradually covered them by its motion, 
they remaining attached to the sun. The corona has also since been 
shown to be a solar appendage. 

Gaseous Nature of the Prominences.— The eclipse of 1868 (July) 
was total in India, and was observed by many skilled astronomers. 
A discovery of M. Janssen's will make this eclipse foi'ever memora- 
ble. He w^as provided with a spectroscope, and by it observed the 
prominences. One prominence in particular was of vast size, and 
when the spectroscope was turned upon it, its spectrum was discon- 
tinuous, showing the bright lines of hydrogen gas. 

The brightness of the spectrum was so marked that Janssen deter- 
mined to keep his spectroscope fixed upon it even after the reappear- 



214 



ASTRONOMY. 




Fia. 63.— ^yN's Corona during the Eclipse of July 29, 18 



TBs: stim 



^15 



ance of sunlight, to see how long it could be followed. It was found 
that its spectrum could still be seen after the return of complete sun- 
light; and not only on that day, but on subsequent days, similar 
phenomena could be observed. 

One great difficulty was conquered in an instant. The red flames 
which formerly were only to be seen for a few moments dui-ing the 
comparatively rare occurrences of total eclipses, and whose observa- 
tion demanded long and expensive journeys to distant parts of the 
world, could now be regularly observed with all the facilities offered 
by a fixed observatory. 

This great step in advance was independently made by Mr. LocE- 




Fia. 64.— Forms of the Solar Prominences as seen with the Spectroscope. 



YER, and his discovery was derived from pure theory, unaided by the 
eclipse itself. By this method the prominences have been carefully 
mapped day by day all around the sun, and it has been proved that 
around this body there is a vast atmosphere of hydrogen gas— the 
chromosphere or sierra. From out of this the prominences are pro- 
jected sometimes to heights of 100,000 kilometres or more. 

It will be necessary to recall the main facts of observation which 
are fundamental in the use of the spectroscope. When a brilliant 
point is examined with the spectroscope, it is spread out by the prism 
into a band — the spectrum. Using two prisms, the spectrum be- 
comes longer, but the light of the surface, being spread over a 



216 ASTRONOMY. 

greater area, is enfeebled. Three, four, or more prisms spread out 
the spectrum proportionally more. If the spectrum is of an incan- 
descent solid or liquid, it is always continuous, and it can be en- 
feebled to any degree; so that any part of it can be made as feeble as 
desired. 

Tliis metliod is precisely similar in principle to the use of the tele- 
scope in viewing stars in the daytime. The telescope lessens the 
brilliancy of tlie sky, while the disk of the star is kept of the same 
intensity, as it is a point in itself. It thus becomes visible. The 
spectrum of a glowing gas will consist of a definite number of lines, 
say three — A, B, C, for example. Now suppose the spectrum of this 
gas to be superposed on the continuous spectrum of the sun; by 
using only one prism, the solar spectrum is short and brilliant, and 
every part of it may be more brilliant than the line spectrum of the gas. 
By increasing the dispersion (the number of p'-isms), the solar spec- 
trum is proportionately enfeebled. If the ratio of the light of the 
bodies themselves, the sun and the gas, is not too great, the continu- 
ous spectrum may be so enfeebled that the line spectrum will be 
visible when superposed upon it, and the spectrum of the gas may 
then be seen even in the presence of true sunlight. Such was the 
process imagined and successfully carried out by Mr. Lockyer, and 
such is in essence the method of viewing the prominences to-day 
adopted. 

. The Coroaal Spectrum.— In 1869 (August 7th) a total solar eclipse 
was visible in the United Stales. It was probably observed by more 
astronomers tlum any preceding eclipse. Two American astron- 
omers, Professor Young, of Dartmouth College, and Professor Hark- 
NESS, of the Naval Observatory, especially observed the spectrum of 
the corona. This spectrum was found to consist of one faint green- 
ish line crossing a faint continuous spectrum. The place of this line 
in the maps of the solar spectrum published by Kirchhoff was oc- 
cupied by a line which he had attributed to the iron spectrum, and 
which had been numbered 1474 in his list, so that it is now spoken 
of as 1474 K. This line is probably due to some gas which must be 
present in large and possibl}^ variable quantities in the corona, and 
which is not known to us on the earth, in this form at least. It is 
probably a gas even lighter than hydrogen, as the existence of this 
line has been traced 10' or 20' from the sun's limb nearly all around 
the disk. 

In the eclipse of July 29th, 1878, which was total in Colorado and 
Texas, the continuous spectrum of the corona was found to be 
crossed by the dark lines of the solar spectrum, showing that the 
coronal li^ht was composed in part of reflected sunlight. 



THE Stlir. 217 

SOUHCES OF THE SUN'S HeAT. 

Theories of the Sun's Constitution. — No considerable 
fraction of tlie heat radiated from the sun returns to it 
from the celestial spaces. But we know tlie sun is daily 
radiating into space 2,170,000,000 times as much heat as 
is daily received by the earth, and it follows that unless 
the supply of heat is infinite (which avc cannot believe) this 
enormous daily radiation must in time exhaust the su])ply. 
When the sujiply is exhausted, or even seriously trenched 
upon, the result to the inhabitants of the earth will be fatal. 
A slow diminution of the daily supply of heat would pro- 
duce a slow change of climates from hotter toward colder. 
The serious results of a fall of 50° in the mean annual tem- 
perature of the earth will be evident wlien we remember 
that such a fall would change the climate of France to that 
of S])itzbergen. The temperature of the sun cannot be 
kept up by the mere combustion of its materials. If the 
sun were solid carbon, and if a constant and adequate supply 
of oxygen were also present, it has been shown that, at the 
present rate of radiation, the heat arising from the com- 
bustion of the mass would not last more than 6000 3'ears. 

An explanation of the solar heat and light lias been siicrgested, 
whicli depends upon the fact that great amounts of heat and light 
are produced by the collision of two rapidly moving heavjMjodies, 
or even by the passage of a heavy body like a meteorite through the 
earth's atmosphere. In fact, if we had a certain mass available with 
which to produce heat in the sun, and if this mass were of the best 
possible materials to produce heat by burning, it can be shown that, 
by burning it at the surface of the sun. we should produce vastly 
less heat than if we simply allowed it to fall into the sun. In the 
last case, if it fell from the earth's distance, it would give 6000 times 
more heat by its fall than by its burning. 

The Uast velocity with which a body from space could fall upon 
t^e sun's surface is in the neighborhood of 280 miles in a second of 



218 ASTRONOMY. 

time, and the velocity may be as great as 350 miles. The meteoric 
theory of solar heat is in effect that the heat of the sun is kept up by 
the impact of meteors upon its surface. 

No doubt immense numbers of meteorites fall into the sun daily 
and hourly, and to each one of them a certain considerable portion 
of heat is due. It is found that, to account for the present amount of 
radiation, meteorites equal In mass to the whole earth would have to 
fall into the sun every century. It is extremely improbable that a 
mass one tenth as large as this is added to the sun in this way per 
century, if for no other reason because the earth itself and every 
planet would receive far more than its present share of meteorites, 
and would become quite hot from this cause alone. 

There is still another way of accounting for the sun's constant 
supply of energy, and this has the advantage of appealing to no cause 
outside of the sun itself in the explanation. It is by supposing the 
heat, light, etc., to be generated by a constant and gradual contrac- 
tion of the dimensions of the solar sphere. As the globe cools hy 
radiation into space, it must contract. In so contracting its ultimate 
constituent parts are drawn nearer together by their mutual attrac- 
tion, whereby a form of energy is developed which can be trans- 
formed into heat, light, electricity, or other physical forces. 

This theory is in complete agreement with the known laws of 
force. It also admits of precise comparison with facts, since the 
laws of heat enable us, from the known amount of heat radiated, to 
infer the exact amount of contraction in inches which the linear 
dimensions of the sun must undergo in order that this supply of heat 
may be kept unchanged, as it is practically found to be. With the 
present size of the sun, it is found that it is only necessary to sup- 
pose that its diameter is diminishing at the rate of about 220 feet per 
year, or 4 miles per century, in order that the supply of heat radiated 
shall be constant. It is plain that such a change as this may be 
taking place, since we possess no instruments sufficiently delicate to 
have detected a change of even ten times this amount since the in- 
vention of the telescope. 

It may seem a paradoxical conclusion that tlie cooling of a body 
may cause it to become hotter. This indeed is true only when we 
suppose the interior to be gaseous, and not solid or liquid. It is, 
however, proved by theory that this law holds for gaseous masses. 

We cannot say whether the sun has yet begun to liquef| 
in his interior parts^ and hence it is impossible to predict; 
at present the duration of his constant radiation. Theory 



THE SVm 219 

shows us that after about 5,000,000 years, the sun radiat- 
ing heat as at present, and still remaining gaseous, will be 
reduced to one half of his present yolume. It seems prob- 
able that somewhere about this time the solidification will 
have begun, and it is roughly estimated, from this line of 
argument, that the present conditions of heat radiation 
cannot last greatly oyer 10,000,000 years. 

The future of the sun (and hence of the earth) cannot, 
as we see, be traced with great exactitude. The past can 
be more closely followed if we assume (which is tolerably 
safe) that the sun up to the present has been a gaseous and 
not a solid or liquid mass. Four hundred years ago, then, 
the sun was about 16 miles greater in diameter than now; 
and if we suppose this process of contraction to have regu- 
larly gone on at the same rate (an uncertain supposition), 
we can fix a date when the sun filled any given space, out 
even to the orbit of Neptune; that is, to the time when 
the solar system consisted of but one body, and that a gas- 
eous or nebulous one. It will subsequently be seen that 
the ideas here reached a j^osteriori have a striking analogy 
to the a priori ideas of Kant and La Place. 

It is not to be taken for granted, however, that the 
amount of heat to be derived from the contraction of the 
sun's dimensions is infinite, no matter how large the prim- 
itive dimensions may have been. A body falling from any 
distance to the sun can only have a certain finite velocity 
depending on this distance and the mass of the sun itself, 
which, even if the fall be from an infinite distance, cannot 
exceed, for the sun, 350 miles per second. In the same 
way the amount of heat generated by the contraction of the 
sun's volume from any size to any other is finite and not 
infinite. 



220 A8TE0N0MY. 

It has been shown that if the sun has always been raclU 
ating heat at its present rate, and if it had originally filled 
all space, it has required 18,000,000 years to contract to its 
present volume. In other words, assuming the present 
rate of radiation, and taking the most favorable case, the 
age of the sun does not exceed 18,000,000 years. Tlie 
eartli is, of course, less aged. The supposition lying at 
the base of tliis estimate is tliat the radiation of the sun 
has been constant throughout the whole period. This is 
quite unlikely, and any changes in this datum affect greatly 
the final number of years wliich we have assigned. While 
this numher may be greatly in error, yet the method of 
obtaining it seems, in the present state of science, to be 
satisfactory, and the main conclusion remains that the past 
of the sun is finite, and that in all probability its future is 
a limited one. The exact number of centui-ies that it is to 
last are of no moment even were the data at hand to obtain 
them: the essential point is that, so far as we can see, the 
sun, and incidentally the solar system, has a finite past and 
a limited future, and that, like other natural objects, it 
passes through its regular stages of birth, vigor, decay, and 
death, in one order of progress. 



CHAPTER III. 



THE INFERIOR PLANETS. 



Motions and Aspects. 



The inferior planets are those whose orbits lie between the sun 
and the orbit of the earth. Coranieucing with the more distant ones, 
they comprise Vejius and Mercury. 

The real and apparent motions of these planets have already been 
briefly described in Part I., Chapter V. It will be remembered that, 
in accordance with Kepler's third law, their periods of revolution 
around the sun are less than that of the earth. Consequently they 
overtake the latter between successive inferior conjunctions. 

The interval between these 
conjunctions is about four 
months in the case of Mer- 
cury, and between nineteen 
and twenty months in that of 
Venus. At the end of this 
period each repeats the same 
series of motions relative to 
the sun. What these motions 
are can be readily seen by 
studying Fig. 65. In the first 
place, suppose the earth at 
any point, E, of its orbit, and 
if we draw a line, E L ov 
EM, from E, tangent to the 

orbit of either of these planets, P^^ g^ 

it is evident that the angle 

which this line makes with that drawn to the sun is the greatest 
elongation of the planet from the sun. The orbits being eccentric, 
this elongation varies with the position of the earth. In the case 
of Mercury it ranges from 16° to 29°, while in the case of Venus, the 
orbit of which is nearly circular, it varies very little from 45°. These 
planets, therefore, seem to have an oscillating motion, first swinging 





222 ABTRONOMT. 

toward the east of the sun, and then toward the west of it, as already 
explained. Since, owing to the annual revolution of the earth, the 
sun has a constant eastward motion among the stars, these planets 
must have, on the whole^ a corresponding though intermittent motion 
in the same direction. Therefore the ancient astronomers supposed 
their period of revolution to be one year, the same as that of the 
sun. 

If, again, we draw a line E8 C from the earth through the sun, the 
point /, in which this line cuts the orbit of the planet, or the point 
of inferior conjunction, will be the least distance of the planet from 

the earth, while the second point C, 
or the point of superior conjunction, 
on the opposite side of the sun, will 
be the greatest distance. Owing to 
the difference of these distances the 
apparent magnitude of these planets, 
as seen from the earth, is subject to 
Fig. 66.— Apparent Magnitubes great variations. 

OF THE DISK OF MERCURY. j.j^ gg gj^^^.g ^^^^^^ variatious in the 

case of Mercury, A representing its apparent magnitude when at its 
greatest distance, 5 when at its mean distance, and Cwhen at its 
least distance. In the case of Venus (Fig. 67) the variations are much 
greater than in that of Mercury, the greatest distance, 1.72, being 
more than six times the least distance, which is only 0.28. The 
variations of apparent magnitude are therefore great in the same 
proportion. 

In thus representing the apparent angular magnitude of these 
planets, we suppose their whole disks to be visible, as they would be 
if they shone by their own light. But since they can be seen only by 
the reflected light of the sun, only those portions of the disk can be 
seen which are at the same time visible from the sun and from the 
earth. A very little consideration will show that the proportion of 
the disk which can be seen constantly diminishes as the planet ap- 
proaches the earth, and looks larger. 

When the planet is at its greatest distance, or in superior conjunction 
((7, Fig. 65), its whole illuminated hemisphere can be seen from the 
earth. As it moves around and approaches the earth, the illuminated 
hemisphere is gradually turned from us. At the point of greatest 
elongation, M or L, one half the hemisphere is visible, and the 
planet has the form of tlie moon at first or second quarter. As it 
approaches inferior conjunction, the apparent visible disk assumes 
the form of a crescent, which becomes thinner and thinner as the 
planet approaches the sun. 



THE INFERIOR PLANETS. 



223 



Fig. 68 shows the apparent disk of Mercury at various times during 
its synodic revolution. Tlie planet will appear brightest when this 
disk has the greatest surface. This occurs about half way between 
greatest elongation and inferior conjunction. 

In consequence of the changes in the brilliancy of these planets 
produced by the variations of distance, and those produced by the 




Fig. 67.— Apparent Magnitudes of the Disk op Venus. 

variations in the proportion of illunr.inated disk visible from the 
earth, partially compensating each other, their actual brilliancy is 
not subject to such great variations as might have been expected. 
As a general rule, Mercury shines with a light exceeding that of a 
star of the first magnitude. But owing to its proximity to the sun, 



A 



• ► ) ) 



B c 



• < C C 



Fig. 68.— Appearance of Mercury at Different Points of its Orbit. 

it can never be seen by the naked eye except in the west a short time 
after sunset, and in the east a little before sunrise. It is then of 
necessity near the horizon, and therefore does not seem so bright as 
if it were at a greater altitude. In our latitudes we might almost 
say that it is never visible! except in the moroing or evening twilight. 



224 ASTRONOMY. 

On the other hand, the planet Venus is, next to the sun and moon, 
the most brilliant object in the heavens. It is so much bii.L^hter 
than any fixed star that there can seldom be any difficulty in identi- 
fying it. The unpractised observer might under some circumstances 
find a difficulty in distinguishing between Venus and Jupiter, but 
the different motions of the two planets will enable him to distin- 
guish them if they are watched from night to night during several 
weeks. 

Atmosphere and Rotation of MERCxmY. 

The various phases of Mercury, as dependent upon its yarious 
positions relative to the sun, have already been shown. If the planet 
were an opaque sphere, without inequalities and without an atmos- 
phere, the apparent disk would always be bounded by a circle on 
one side and an ellipse on the other, as represented in the figure. 
Whether any variation from this simple and perfect form has ever 
been detected is an open question, the balance of evidence being very 
strongly in the negative. Since no spots are visible upon it, it would 
follow that unless variations of form due to inequalities on its sur- 
face, such as mountains, can be detected, it is impossible to deter- 
mine whether the planet rotates on its axis. 

We may regard it as doubtful whether any evidence of an atmos- 
phere of Mercury has been obtained, and it is certain that we know 
nothing definite respecting its physical constitution. 

Atmosphere and Rotation of Venus. 

As Venus sometimes comes nearer the earth than any other pri- 
mary planet, astronomers have examined its surface with great at- 
tention ever since the invenlion of the telescope. But no conclusive 
evidence respecting the rotation of the planet and no proof of any 
changes or any inequalities on its surface have ever been obtained. 

Atmosphere of Venus. — The evidence of an atmospliere of Venus is 
jXM-haps more conclusive than in the case of any other planet. 
When Venus is observed very near its inferior conjunction, and 
when it therefore presents the view of a very thin crcsrent, it is 
found that this crescent extends over more tiian 180°. This would 
be evidently impossible unless the sun illuminated more than one 
half the planet. We therefore conclude that Venus h^s an atmos- 
phere which exercises so powerful a refraction upon the light of the 
sun that the latter illuminates several degrees more than one half the 
globe. A phenomenon which must be attributed to the same cause 
h^s seyeral times bpqn observed during transits of Venus, During 



THE INFERIOR PLANETS. 225 

the transit of December 8th, 1874, most of the observers who enjoyed 
a fine steady atmosphere saw that when Venus was partially pro- 
jected on the sun, the outlitie of that part of its disk outside the sun 
could be distinguished by a delicate line of light. From these 
several observations it would seem that the refractive power of the 
atmosphere of Venus is greater than that of the earth. 

Teansits of Mebcuky and Venus. 

When Mercury or Venus passes between the earth and sun, so as 
to appear projected on the sun's disk, the phenomenon is called a 
transit. If these planets moved around the sun in the plane of the 
ecliptic, it is evident that there would be a transit at every inferior 
conjunction. 

The longitude of the descending node of Mercury at the present 
time is 227°, and therefore that of the ascending node 47°. The 
earth has these longitudes on May 7lh and November 9th. Since a 
transit can occur only within a few degrees of a node, Mercury cau 
transit only within a few days of these epochs. 

The longitude of the descending node of Venua is now about 256" 
and therefore that of the ascending node is 76°. The earth has these 
longitudes on June 6th and December 7th of each year. Transits of 
Venus can therefore occur only within two or three days of these 
times. 

Kecurrence of Transits of Mercury. — The following table shows the 
dates of occurrence of transits of Mercury during the present cen- 
tury. They are separated into May transits, which occur near the 
descending node, and November ones, which occur near the ascend- 
inu: node. November transits are the most numerous, because 
Mercury is then nearer the sun, and the transit limits are wider. 

1799, May 6. 1802, Nov. 9. 

1832, May 5. 1815, Nov. 11. 

1845. May 8. 1822, Nov. 5. 

1878. May Q. 1835. Nov. 7. 

1891, May 9. 1848. Nov. 10. 

1861, Nov. 12. 

1868. Nov. 5. 

1881, Noy. 7. 

1894, Nov. 10. 

BecTirrence of Transits of Venus. — For many centuries past and to 
QQijie, tr<'^ps|ts of Venus occur iu a cycle more exact \^^n t?^P?e of 



226 ASTRONOMY. 

Mercury. It happens that Venus makes 13 revolutions around the 
sun in nearly the same time that the earth makes 8 revolutions; that 
is, in eight years. During this period there will be 5 inferior con- 
junctions of Venus, because the latter has made 5 revolutions more 
than the earth. Consequently, if we wait eight years from an inferior 
conjunction of Venus, we shall, at the end of that time, have another 
inferior conjunction, the fifth in regular order, at nearly the same 
point of the two orbits. It will, therefore, occur at the same time 
of the year, and in nearly the same position relative to the node of 
Venus. 

After a pair of transits 8 years apart, an interval of over 100 years 
must elapse before the occurrence of another pair as is shown in the 
following table. The dates and intervals of the transits for three 
cycles nearest to the present time are as follows: 

Intervals. 
1518, June 2. 1761, June 5. 2004, June 8 8 years. 

1526, June 1. 1769, June 3. 2012, June 6. 105i " 

1631, Dec. 7. 1874, Dec. 9. 2117, Dec. 11. 8 " 

163V, Dec. 4. 1882, Dec. 6. 2125, Dec. 8 121i " 

Supposed Intramercurial Planets. 

Some astronomers are of opinion that there is a small planet or 
a group of planets revolving around the sun inside the orbit of 
Mercury. To this supposed planet the name Vulcan has been given; 
but astronomers generally discredit the existence of any such planet 
of considerable size. 

The evidence in favor of the existence of such planets may be 
divided into three classes, as follows, which will be considered in 
their order: 

(1) A motion of the perihelion of the orbit of Mercury, supposed 
to be due to the attraction of such a planet or group of planets. 

(2) Transits of dark bodies across the disk of the sun which have 
been supposed to be seen by various observers during the past cen- 
tury. 

(3) The observation of certain unidentified objects by Professor 
Watson and Mr. Lewis Swift during the total eclipse of the sun, 
July 29th, 1878. 

(1) In 1858 Le Verrier made a careful collection of all the obser- 
vations on the transits of Mercury which had been recorded since the 
invention of the telescope. The result of that investigation waa 



THE INFEBIOR PLANETS. 227 

that the observed times of transit could not be reconciled with the 
calculated motion of the planet, as due to the gravitation of the 
other bodies of the solar system. He found, however, that if, in 
addition to the changes of the orbit due to the attraction of the 
known planets, he supposed a motion of the perihelion amountiDg to 
36 ' iu a century, the observations could all be satisfied. Such a 
motion might be produced by the attraction of an unknown planet 
inside the orbit of Mercury. Since, however, a single planet, in 
order to produce this effect, would have to be of considerable size, 
and since no such object had ever been observed during a total 
eclipse of the sun, he concluded that there was probably a group of 
planets much too small to be separately distinguished. 

(2) It is to be noted that if such planets existed they would fre- 
quently pass over the disk of the sun. During the past fifty years 
the sun has been observed almost every day with the greatest 
assiduity by eminent observers, armed with powerful instruments, 
who have made the study of the sun's surface and spots the principal 
work of their lives. None of these observers has ever recorded the 
transit of an unknown planet. This evidence, though negative in 
form, is, under the circumstances, conclusive against the existence 
of such a planet of such magnitude as to be visible in transit with 
ordinary instruments. 

(3) The observations of Professor Watson during the total eclipse 
above mentioned seem to afford the strongest evidence yet obtained 
in favor of the real existence of the planet. His mode of proceeding 
was briefly this: Sweeping to the west of the sun during the eclipse, 
he saw two objects in positions where, supposing the pointing of his 
telescope accurately known, no fixed star existed. There is, how- 
ever, a pair of known stars, one of which is about a degree distant 
from one of the unknown objects, and the other about the same 
distance and direction from the second. It is probable that Professor 
Watson's supposed planets were this pair of stars. 

Since the above was written Prof. Watson's observations have 
been repeated under exceptionally favorable circumstances at the 
eclipse of May 6, 1883, and no trace of his supposed planets was seen, 
while much smaller stars were observed. 



CHAPTER lY. 

THE MOON. 

Wheit it became clearly understood that the earth and 
moon were to be regarded as bodies of one class, and that 
the old notion of an impassable gulf between the character 
of bodies celestial and bodies terrestrial was unfounded, 
the question whether the moon was like the earth in all its 
details became one of great interest. The point of most 
especial interest was whether the moon could, like the 
earth, be peopled by intelligent inhabitants. Accordingly, 
Avhen the telescope was invented by Galileo, one of the 
first objects examined was the moon. With every im- 
provement of the instrument the examination became 
more thorough, so that at present the topography of the 
moon is much better known than that of the State of 
Arkansas, for example. 

With every improvement in the means of research, it 
has become more and more evident thnt the surface of the 
moon is totally unlike that of our earth. There are no 
oceans, seas, rivers, air, clouds, or vapor. We can hardly 
suppose that animal or vegetable life exists under such cir- 
cumstances, the fundamental conditions of such existence 
on our earth being entirely wanting. We might almost as 
well suppose a piece of granite or lav^ to be the abode of 
life as the surface of the moon. 

^Ue length of one mile on the moon would, as mm from 



THE MOON, 229 

the earth, subtend an angle of about 1" of arc. More 

exactly, the angle subtended would range between 0".8 and 

0^9, according to the varying distance of tlie moon. In 

order that an object may be plainly visible to the naked 

eye, it must subtend an angle of nearly V. Consequently 

a magnifying power of 60 is required to render a round 

object one mile in diameter on the surface of the moon 

plainly visible. Starting from this fact, we may readily 

form the following table, showing the diameters of the 

smallest objects that can be seen with different magnifying 

powers, always assuming that vision with these powers is 

perfect: 

Power 60 ; diameter of object 1 mile. 
Power 150; diameter 2000 feet. 
Power 500; diameter 600 feet. 
Power 1000; diameter 300 feet. 
Power 2000; diameter 150 feet. 

If telescopic power could be increased indefinitely, there 
would of course be no limit to the minuteness of an object 
visible on the moon's surface. But the necessary imper- 
fections of all telescopes are such that only in extraordinary 
cases can anything be gained by increasing the magnifying 
power beyond 1000. The influence of warm and cold cur- 
rents in our atmosphere will forever prevent the advan- 
tageous use of high magnifying powers. After a certain 
limit we see nothing more by increasing the power, vision 
becoming indistinct in proportion as the power is increased. 
It is hardly likely that an object less than 600 feet in extent 
can ever be seen on the moon by any telescope whatever, 
unless it becomes possible to mount the instrument above 
the atmosphere of the earth. It is therefore only the great 
features on the surface of the moon, and not the minute 
gnes, which can be m^<^e out with the telescope, 



230 



ASTRONOMY. 




— Aspect of the Moon's Surface. 



Character of the Moon's Surface.— The most striking point of dif- 
ference between tlie earth and moon is seen in the total absence from 
the latter of anything that looks like an undulating surface. No 



THE MOOK 231 

formations similar to our valleys and mountain-chains have been 
detected. The lowest surface of the moon which can be seen with 
the telescope appears to be nearly smooth and flat, or, to speak 
more exactly, spherical (because the moon is a sphere). This sur- 
face has different shades of color in different regions. Some por- 
tions are of a bright silvery tint, while others have a dark gray ap- 
pearance. These differences of tint seem to arise from differences of 
material. 

Upon this surface as a foundation are built numerous formations 
of various sizes, but all of a very simple character. Their general 
form can be made out by the aid of Fig. 69, and their dimensions by 
the scale of miles at the bottom of it. The largest and most promi- 
nent features are known as craters. They have a typical form con- 
sisting of a round or oval rugged wall rising from the plane in the 
manner of a circular fortification. These walls arc frequently from 
three to six thousand metres in height, very rough and broken. In 
their interior we see the plane surface of the moon already described. 
It is, however, generally covered with fragments or broken up by 
small inequalities so as not to be easily made out. In the centre of 
the craters we frequently find a conical formation rising up to a con- 
siderable height, and much larger than the inequalities just described. 
In the craters we have a vague resemblance to volcanic formations 
upon the earth, the principal difference being that their magnitude is 
very much greater than anything known here. The diameter of the 
larger ones ranges from 50 to 200 kilometres, while the smallest are 
so minute as to be hardly visible with the telescope. 

When the moon is only a few days old, the sun's rays strike very 
obliquely upon the lunar mountains, and they cast long shadows. 
From the known position of the sun, moon, and earth, and from the 
measured length of these shadows, the heights of the mountains can 
be calculated. It is thus found that some of the mountains near the 
south pole rise to a height of 8000 or 9000 metres (from 25,000 or 30,000 
feet) above the general surface of the moon. Heights of from 3000 
to 7000 metres are very common over almost the whole lunar surface. 

The question of the origin of the lunar features has a bearing on 
theories of terrestrial geology as w^ell as upon various questions re- 
specting the past history of the moon itself. It has been considered 
in this aspect by various geologists. 

Lunar Atmosphere. — The question whether the moon has an atmos- 
phere has been much discussed. The only conclusion which has yet 
been reached is that no positive evidence of an atmosphere has ever 
been obtained, and that if one exists it is certainly several hundred 
times rarer than the atmosphere of our earth. 



232 ASTRONOMY. 

Light and Heat of the Moon. — Many attempts have been made to 
measure the ratio of the light of the full moon and that of the sun. 
The results have been very discordant, but all have agreed in show- 
ing that the sun emits several hundred thousand times as much light 
as the full moon. The last and most careful determination is that of 
ZoLLNER, who finds the sun to be 618,000 times as bright as the full 
moon. 

Tiie moon must reflect the heat as well as the light of the sun, and 
must also radiate a small amount of its own heat. By collecting the 
moon's rays in the focus of one of his large reflecting telescopes, Lord 
RossE was able to show that a certain amount of heat is actually 
received from the moon, and that this amount varies with the moon's 
phase, as it should do. As a general result of all his researches, it 
may be supposed that about six sevenths of the heat given out by the 
moon is radiated and one seventh reflected. 

Is there any Change on the Surface of the Moon *? — When the sur- 
face of the moon was first found to be covered by craters having the 
appearance of v61canoes at the surface of the earth, it was very 
naturally thought that these supposed volcanoes might be still in 
activity, and exhibit themselves to our telescopes by their flames. 
Not the slightest sound evidence of any incandescent eruption at the 
moon's surface has been found, however. 

Several instances of supposed changes of shape of features on the 
moon's surface have been described in recent times. 

The question whether these changes are proven is one on which 
the opinions of astronomers differ. The difficulty of reaching a cer- 
tain conclusion arises from the fact that each feature necessarily 
varies in appearance, owing to the different directions in which the 
sun's light falls upon it. Sometimes the changes are very difficult 
to account for, even when it is certain that they do not arise from 
any change on the moon itself. Hence while some regard the appa- 
rent changes as real, others regard them as due only to differences in 
the mode of illumination. 



CHAPTER V. 
THE PLANET MAKS. 

Description of the Planet. 

Mars is the next planet beyond the earth in the order of 
distance from the sun, being about half as far again as the 
earth. It has a decided red color, by which it may be 
readily distinguished from all the other planets. Owing to 
the considerable eccentricity of its orbit, its distance, both 
from the sun and from the earth, varies in a larger propor- 
tion than does that of the other outer planets. 

At the most favorable oppositions, its distance from the 
earth is about 0.38 of the astronomical unit, or, in round 
numbers, 57,000,000 kilometres (35,000,000 of miles). 
This is greater than the least distance of Venus, but we 
can nevertheless obtain a better vicw^ of Mars under these 
circumstances than of Venus, because when the latter is 
nearest to us its dark hemisphei'e is turned toward u-. 
while in the case of Mars and of the outer planets tie 
hemisphere turned toward us at op])osition is fully illumi- 
nated by the sun. 

The period of revolution of 3fars around the sun is a 
little less than two years, or, more exactly, 6S7 days. The 
successive oppositions occur at intervals of two years and 
one or two months, the earth having made during this in- 
terval a little more than two revolutions around the sun, 
and the planet Mars a little more than one. The dates of 



234 ASTBOXOJfT. 

acTeral past and futare oppodnons are shoTm in the fol- 
io virr Ta:lr: 

iSi: December 26dL 

1 S'>4 Jamianr 31st. 

1 S >5 March 6Ui. 



0~::ir :: :ne une<^nai motion oi the planet, arifdng from 
the e^cciiiTcity of its orbit, the interrals between gncces- 
siTe oppositions Taiy from two years and one month to two 
years ini ~.~o and a half months. 

1 T rsaarily exhibits phases, but they are not so well 
::^„:^r^ :.5 :n the case of Venus, becaose the hemisphere 
which i: r:ese:i:s '.:• :Jic observer on the earth is always 
more thii. . :* :: ;.:etL The greatest phase occurs 
when its d-e-:: lo- s rv I'rm Th:u of the sun, and even 
then sx seTentiis of Ils dis^ i; L. niinared, like ihst of the 
moon, three days before or aitcr t\ m::::. The phases 
of Mars were observed by Gaxtlz : i. i.i.. 

BoTitiCT «£ Mara. — The early teles ? : ; t -f ; - : : : t : ±i' *i = 

disk of Mars did not appear unii : z : i . t i 

had a Tazi^aled asp*ert. In If^f I: ?. hit H ^l^ : _ _ _ . 
the markings on Jfc'^i ^rrf irri^-i: ii. : -lirui is : i 
war as to ^how ^lax iLf :^:.i.t: :t~ t " :. : - iz s 7^ 1.^5 

girai in hk drawirrf ;ii f : Zri :. 7 Ti^ : z t 

made use of to detemlzr ._i fz: : zr z : - 

Sowdl is the rota:::z zi-i 7 - s : t z 

detomine the exac: : :^ i z z . 5 : z r 

axis since tliese old .f T_ z ^ t_ 

found to be 3^B> 2i'.: : z r : 

twotenths cf s seczzi I: . _ :t ^S: :_:.z zl ^ -^z:. t: 

than the P'f: : : ; :. : z : : 

Snfiue c: :^i:5 — T_t ziz i zr resolt oi these markings 

on Mart li :_ t _ 5 . _ 7 t : ^ diTerEified by land and 

waier. cc^t.tZ _ .._ . .zt z zz : _z'_^r "verv similar to the 

san&Zz :: :z.t . ;_ ^ z i ; : z. : _ . .;?arc of a decided 
r^ic:":: :^z __5 _ r : ;t -? -7 aspect of the 

Z-:.zt: ; :z.t: ; z::. :.:7 ; : ;. . tv_ ■ :iierefore sup- 

z T_ : T i^ ^ T_7 z. ^ ^ _ : 7 7 - . brilliant while 



THE PLAyET MARS. 235 

regions, one lying around each pole of the planet. It has been sup- 
posed that this appearance is due to immense masses of snow and 
ice surrounding the poles. If this were so, it would indicate that 
the processes of evaporation, cloud formation, and condensation of 
vapor into rain and snow go on at the surface of Mars as at the sur- 
face of the earth. A certain amount of color is given to this theory 
by supposed changes in the magnitude of these ice-caps. But the 
problem of establishing such changes is one of extreme difficulty. 
The only way in which an adequate idea of this difficulty can be 
formed is by the student himself looking at Mars through a telescope. 
If he will then note how hard it is to make out the different 
shades of light and darkness on the planet, and how they must vary in 
aspect under different conditions of clearness in our own atmosphere, 
he will readily perceive that much evidence is necessary to establish 
great changes. All we can say, therefore, is that the formation of 
the ice-caps in winter and their melting in summer has some evi- 
dence in its favor, but is not yet completely proven. 

Satellites of Mars. 

Until the year 1877 Mars was supposed to have no satellites, none 
having ever been seen in the most powerful telescopes. But in 
August of that year Professor Hall, of the Xaval Observatory, 
instituted a systematic search with the great equatorial, which 
resulted in the discovery of two such objects. 

These satellites are by far the smallest celestial bodies known. It is 
of course impossible to measure their diameters, as they appear in 
the telescope only as points of light. The outer satellite is probably 
about six miles and the inner one about seven miles in diameter. 
The outer one was seen with the telescope at a distance from the 
earth of 7,000,000 times this diameter. The proportion would be 
that of a ball two inches in diameter viewed at a distance equal to 
that between the cities of Boston and Xew York. Such a feat of 
telescopic seeing is well fitted to give an idea of the power of modern 
optical instruments. 

Professor Hall found that the outer satellite, which he called 
Deimos, revolves around the planet in SO'' IB"", and the inner one, 
called Phobos, in 7'" 38"". The latter is only 5800 miles from the 
centre of Mars, and less than 4000 miles from its surface. It would 
therefore be almost possible with one of our telescopes on the sur- 
face of Mars to see an object the size of a large animal on the 
satellite. 

This short distance and rapid revolution make the inner satellite 



^36 



ASTBONOMf. 



of Mars one of the most interesting bodies with which we are ac- 
quainted. It performs a revolution in its orbit in less than half the 
time that Mars revolves on its axis. In consequence, to the inhab- 
itants of Mars it would seem to rise in the west and set in the east. 
It will be remembered that the revolution of the moon around the 
earth and of the earth on its axis are both from west to east: but the 




Fig. 70.— Telescopic Vnrw op Mars. 



latter revolution being the more rapid, the apparent diurnal motion 
of the moon is from east to west. In the case of the inner satellite 
of Mars, however, this is reversed, and it tlierefore appears to move 
in the actual direction of its orbital motion. The rapidity of its 
phases is also equally remarkable. It is less than two hours from 
new moon to first quarter, and so on. Thus the inhabitants of Mars 
may see their inner moon pass through all its phases from new to 
full and again to new in a sins-le uiarht. 



CHAPTER VI. 
THE MINOR PLANETS. 

When" the solar system was first mapped out in its true 
proportions by Copernicus and Kepler, only six primary 
planets were known; namely. Mercury, Venus, the Earth, 
Mars, Jupiter, and Saturii. These succeeded each other 
according to a nearly regular law, as we have shown in 
Chapter I., except that between Mars and Jupiter a gap 
was left where an additional planet might be inserted, 
and the order of distances be thus made complete. It was 
therefore supposed by the astronomers of the seventeenth 
and eighteenth centuries that a planet might be found in 
this region. A search for this object was instituted to- 
ward the end of the last century, but before it had made 
much progress a planet in the place of the one so long 
expected was found by Piazzi, of Palermo. The discov- 
ery was made on the first day of the present century, 1801, 
January 1st. 

In the course of the following seven years the astronom- 
ical world was surprised by the discoveiy of three other 
planets, all in the same region, though not revolving in 
the same orbits. Seeing four small planets where one 
large one ought to be, Olbers Avas led to his celebrated 
hypothesis that these bodies were the fragments of a large 
planet which had been broken to pieces by the action of 
some unknown force. 



238 ASTRONOMY. 

A generation of astronomers now passed away without 
the discovery of more than these four. In 1845 a fifth 
planet of the group was found. In 1847 three more were 
discovered, and discoveries have since been made at a rate 
which thus far sliows no signs of diminution. The num- 
ber has now reached 225, and the discovery of additional 
ones seems to be going on as fast as ever. The frequent 
announcements of the discovery of planets which appear 
in the public prints all refer to bodies of this group. 

The minor planets are distinguished from the major 
ones by many characteristics. Among these we may men- 
tion their small size; their positions, all being situated be- 
tween the orbits of Mars and Jupiter; the great eccentrici- 
ties and inclinations of their orbits. 

Number of Small Planets. — It would be interesting to know how 
many of these planets there are in all, but it is as yet impossible even 
to guess at the number. As already stated, fully 200 are now 
known, and the number of new ones found every year ranges from 
7 or 8 to 10 or 12. If ten additional ones are found every year dur- 
ing the remainder of the century, 400 will then have been dis- 
covered. 

A minor planet presents no sensible disk, and therefore looks ex- 
actly like a small star. It can be detected only by its motion among 
the surrounding stars, which is so slow that hours must elapse before 
it can be noticed. 

Magnitudes. — It is impossible to make any precise measurement of 
the diameters of the minor planets. These can, however, be esti- 
mated by the amount of light which the planet reflects. Supposing 
the proportion of light reflected about the same as in the case of the 
larger planets, it is estimated that the diameters of the three or four 
largest, which are tliose first discovered, range between 300 and 600 
kilometres, while the smallest are probably from 20 to 50 kilometres 
in diameter. Tlie average diameter of all that are known is perhaps 
less than 150 kilometres; that is, scarcely more than one hundredth 
that of the earth. The volumes of solid bodies vary as the cubes of 
their diameters; it might tliereforc take a million of these planets to 
make one of the size of the earth. 



THE MINOR PLANETS. 239 

Form of Orbits. — The orbits of the minor planets are much more 
eccentric than those of the larger ones; their distance from the sun 
therefore varies very widely. 

Origin of the Minor Planets. — The question of the origin of these 
bodies was long one of great interest. The features which we have 
described associate themselves very naturally with the hypothesis 
of Olbers, that we here liave the fragments of a single large planet 
which in the beginning revolved in its proper place between the 
orbits of Mars and Jupiter. No support has been given to Olbers' 
hypothesis by subsequent investigations, and it is no longer consid- 
ered by astronomers to have any foundation. So far as can be judged, 
these bodies have been revolving around the sun as separate planets 
ever since the solar system itself was formed. 



CHAPTER VII. 
JUPITER AND HIS SATELLITES. 

The Planet Jupitee. 

Jupiter is mncli tt\Q largest planet in the system. His 
mean distance is nearly 800,000,000 kilometres (480,000,- 
000 miles). His diameter is 140,000 kilometres, corre- 
sponding to a mean apparent diameter, as seen from the 
sun, of 36". 5. His linear diameter is about -f^, his surface 
is yi-^, and his volume y^Vo that of the sun. His mass is 
y^^, and his density is thus nearly the same as the sun's; 
viz., 0.24 of the earth's. He rotates on his axis in 
9^ 55"^ 20«. 

He is attended by four satellites, which were discovered 
by Galileo on January 7th, 1610. He named them, in 
honor of the Medicis, the Medicean stars. They are 
now known as Satellites I, II, III, and IV, I being the 
nearest. 

The surface of Jupiter has been carefully studied with 
the telescope, particularly within the past twenty years. 
Although further from us than Mars, the details of his 
disk are much easier to recognize. The most characteristic 
features are given in the drawings appended. These 
features are, first, the dark bands of the equatorial 
regions, and, secondly, the cloud-like forms sj^read over 
nearly the whole surface. At the limb all these details 
become indistinct, ^iid finally vanish, thus indicating ^ 



J t PITER AND HIS SATELLITES. 241 

highly absorptive atmosphere. The light from the centre 
of the disk is twice as bright as that from the poles. The 
bands can be seen with instruments no more powerful 
than those used by Galileo, yet he makes no mention of 
them. 

The color of the bands is reddish. The position of the 
bands varies in latitude, and the shapes of the limiting 
curves also change from day to day; but in the main they 
remain as permanent features of the region to which they 
belong. Two such bands are usually visible, but often 




Fig. 71.— Telescopic View op Jupiter and his Satellites. 

more are seen. Herschel, in the year 1793, attributed 
the aspects of the bands to zones of the planet's atmos- 
phere more tranquil and less filled with clouds than the re- 
maining portions, so as to permit the true surface of the 
planet to be seen through these zones, while the prevailing 
clouds in the other regions give a brighter tint to these 
latter. The color of the bands seems to vary from time to 
time, and their bordering lines sometimes alter with such 
rapidity as to show that these borders are formed of some- 
thing like clouds. 
The clouds themselves p^n easily be seen at times, and 



^42 



ASTRONOMY. 



they have every variety of shape, sometimes appearing as 
brilliant circular white masses, but oftener they are similar 
in form to a series of white cumulus clouds such as are 
frequently seen piled up near the horizon on a summer's 
day. The bands themselves seem frequently to be veiled 
over with something like the thin cirrus clouds of our at- 
mosphere. 




Fig. 72. 



-Telescopic View of Jupiter, with a Satellite and its Shadow 
seen on the disk. 



Such clouds can be tolerably accurately observed, and maybe used 
to determine the rotation-time of the planet. These observations 
show that the clouds have often a motion of their own, which is also 
evident from other considerations. 

The following results of observation of spots situated in various 
regions of the planet will illustrate this; 



JUPITER AND HIS SATELLITES. 



^43 



Casstni 1665, 

Herschel 1778, 

Herschel 1779, 

schroeter 1785, 

Beer and Madler . 1835, 

Airy 1835, 

Schmidt 1863. 



h. m. s. 

rotation lime = 9 56 00 

= 9 55 40 

= 9 50 48 

= 9 56 56 

= 9 55 26 

= 9 55 21 

= 9 65 29 




Fio. 73. 

The Satellites of Jupiter. 

Motions of the Satellites. — The four satellites move about Jupiter 
from west to east in nearly circular orbits. When one of these 
satellites passes between the sun and Jupiter, it casts a shadow upon 
Jupiter's disk (see Fig, 73) precisely as the shadow of our moon ia 



244 ASTRONOMY. 

thrown upon the earth in a solar eclipse. If the satellite passes 
tlirough Jupitefs own shadow in its revolution, an eclipse of this 
satellite takes place. If it passes between tlie earth and Jupiter, it 
is projected upon Jupitefs disk, and we have a transit; if Jupiter is 
between the earth and the satellite, an occultation of the latter oc- 
curs. All these phenomena can be seen with a common telescope, 
and the times of observation are all found predicted in the Nautical 
Almanac. These shadows being seen black upon Jupiter's surface, 
show that this planet shines by reflecting the light of the sun. 

Telescopic Appearance of the Satellites. — Under ordinary circum- 
stances, the satellites of Jupiter are seen to have disks; that is, not 
to be mere points of light. Under very favorable conditions, mark- 
ings have been seen on these disks. 

The satellites completely disappear from telescopic view when 
they enter the shadow of the planet. This seems to show that 
neither planet nor satellite is self-luminous to any great extent. If 
the satellite were self-luminous, it would be seen by its own light; 
and if the planet were luminous, the satellite might be seen by the re- 
flected light of the planet. 

The motions of these objects are connected by two curious and 
important relations discovered by La Place, and expressed as fol- 
lows: 

I. The mean motion of the first satellite added to twice the mean mo- 
tion of the third is exactly equal to three times the mean motion of the 
second. 

II. If to the mean longitude of the first satellite we add twice the mean 
longitude of the third, and subtract three times the mean longitude of the 
second, the difference is always 180°. 

The first of these relations is shown in the following table of the 
mean daily motions of the satellites : 

Satellite I in one day moves 203°. 4890 

" II " " 101°.3748 

" III " " 50°. 3177 

" IV " " 21°.5711 

Motion of Satellite I , 203°.4890 

Twice that of Satellite III 100°. 6354 

Sum 304°.1244 

Three times motion of Satellite II 304°. 1244 

Observations showed that this condition was fulfilled as exactly as 
possible, but the discovery of La Place consisted in showing that if 
the approximate coincidence of the mean motions was once estf^lj- 



JUPITER AND HIS SATELLITES. 



245 



lished, they could never deviate from exact coincidence with the 
law. The case is analogous to that of the moon, which always 
presents the same face to us and which always will, since the rela- 
tion being once approximately true, it will become exact and ever 
remain so. 

The discovery of the gradual propagation of light by means of 
these satellites has already been described, and it has also been ex- 
plained that they are of use in the rough determination of longi- 
tudes. To facilitate their observation, the Nautical Almanac gives 
complete ephemerides of their phenomena. A specimen of a portion 
of such an ephemeris for 1865, March 7th, 8th, and 9th, is added. 
The times are Washington mean times. 

1865— March. 









d. 


n. 


m. 


s. 


I 


Eclipse 


Disapp. 


7 


18 


27 


38.5 


I 


Occult. 


Reapp. 


7 


21 


56 




III 


Shadow 


Ingress 


8 


7 


27 




III 


Shadow 


Egress 


8 


9 


58 




III 


Transit 


Ingress 


8 


12 


31 




II 


Eclipse 


Disapp. 


8 


13 


1 


22.7 


III 


Transit 


Egress 


8 


15 


6 




II 


Eclipse 


Reapp. 


8 


15 


24 


11.1 


II 


Occult. 


Disapp. 


8 


15 


27 




I 


Shadow 


Ingress 


8 


15 


43 




I 


Transit 


Ingress 


8 


16 


58 




I 


Shadow 


Egress 


8 


17 


57 




II 


Occult. 


Reapp. 


8 


17 


59 




I 


Transit 


Egress 


8 


19 


13 




I 


Eclipse 


Disapp. 


9 


12 


55 


59.4 


I 


Occult. 


Reapp. 


9 


16 


25 





Suppose an observer near New York City to have determined his 
local time accurately. This is about 13"' faster than Washington 
time. On 1865. March 8th, he would look for the reappearance of 
II at about 15'' 34"* of his local time. Suppose he observed it at 
15'' 36"" 22^7 of his time: then his meridian is 12'" 11^6 east of 
Washington. The difficulty of observing these eclipses with accu- 
racy, and the fact that the aperture of the telescope employed has an 
important effect on the appearances seen, have kept this method 
from a wide utility, which it at first seemed to promise. 



CHAPTER VIII. 
SATURN AND ITS SYSTEM. 

General Description. 

8aUirn is the most distant of the major planets known 
to the ancients. It revolves around the sun in 29^ years, 
at a mean distance of about 1,400,000,000 kilometres 
(882,000,000 miles). The angular diameter of the ball of 
the planet is about 16". 2, corresponding to a true diameter 
of about 110,000 kilometres (70,500 miles). Its diameter 
is therefore nearly nine times and its volume about 700 
times that of the earth. It is remarkable for its small 
density, which, so far as known, is less than that of any 
other heavenly body, and even less than that of water. It 
revolves on its axis in 10^ 14"" 24% or less than half a day. 

Saturn is perhaps the most remarkable planet in the 
solar system, being itself the centre of a system of its 
own, altogether unlike anything else in the heavens. Its 
most noteworthy feature is a pair of rings which surround 
it at a considerable distance from the planet itself. Out- 
side of these rings revolve no less than eight satellites, 
or twice the greatest number known to surround any other 
planet. The planet, rings, and satellites are altogether 
called the Saturnian system. The general appearance of 
this system, as seen in a small telescope, is shown in Fig. 74. 



BATURN AND ITS SYSTEM. 247 

To the naked eye Saturn is of a dull yellowish color, 
shining with about the brilliancy of a star of the first mag- 
nitude. It varies in brightness, however, with the way in 
which its ring is seen, being brighter the wider the ring 
appears. It comes into opposition at intervals of one year 
and from twelve to fourteen days. The following are the 



Fig. 74.— Telescopic Vie\7 of the Saturnian System. 

times of some of these oppositions, by studying which one 
will be enabled to recognize the planet: 

1882 November 14th. 

1883 November 28th. 

1884 December 11th. 

During these years it will be best seen in the autumn 
and winter. 

When viewed with a telescope, the physical appearance 
of the ball of Saturn is quite similar to that of Jupiter, 



^48 AsmomMT. 

haying light and dark belts parallel to the direction of its 
rotation. 

The Rings of Saturn. 

The rings are tlio most remarkable and characteristic feature of 
the Saturnian system. Fig. 75 gives two views of the ball and rings. 
The upper one shows one of their aspects as actually presented in 
the telescope, and the lower one shows what the appearance would 
be if the planet were viewed from a direction at right angles to the 
plane of the ring (whicli it never can be from the earth). 

The first telescopic observers of iSaiurn were unable to see the 
rings in their true form, and were greatly perplexed to account 
for the appearance which the planet pi'esonted. Galileo described 
the planet as " tri-corporate," the two ends of the ring having, in his 
imperfect telescope, the appearance of a pair of small planets at- 
tached to the central one. "On each side of old ^Saturn were ser- 
vitors who aided him on his way." This supposed discovery was 
announced to his friend Kepler in this logogriph: 

"smaismrniilinepoetalevmibunenugttaviras," which, being trans- 
posed, becomes — 

" Altissimum planetam tergeminum observavi" (I have observed 
the most distant planet to be tri-form). 

The phenomenon constantly remained a mystery to its first ob- 
server. In 1610 he had seen the planet accompanied, as he supposed, 
by two lateral stars; in 1612 the latter had vanished and the central 
body alone remained. After that Galileo ceased to observe Saturn. 

The appearances of the ring were also incomprehensible to He- 
velius, Gassendi, and others. It was not until 1655 (after seven 
years of observation) that the celebrated Huyghens discovered the 
true explanation of the remarkable and recurring series of phenom- 
ena present by the tri-corporate planet. 

He announced his conclusions in the following logogriph: 

"aaaaaa ccccc d eeeee g h iiiiiii 1111 mm nnnnnnnnn oooo pp q rr s 
ttttt uuuuu," which, when arranged, read — 

" Annulo cingitur, tonui, piano, nusquam coherente, ad eclipticam 
inclinato" (it is girdled by a thin plane ring, nowhere touching, in- 
clined to the ecliptic). 

This description is complete and accurate. 

In 1675 it was found by Cassini, that what Huyghens had seen 
as a single ring was really two. A division extended all the way 
around near the outer edge. This division is shown in the figures. 

In 1850 the Messrs, Bond, of Harvard College Observatory, found 



SATURN AND ITS SYSTEM. 



24& 




Fig. 75.— Rings of Satuen. 



250 ABTRONOMf. 

that there was a third ring, of a dusky and nebulous aspect, inside the 
other two, or rather attached to tlie inner edge of the inner ring. It 
is therefore known as Bond's dusky ring. It had not been before fully 
described owing to its darkness of color, which made it a difficult 
object to see except with a good telescope. It is not separated from 
the bright ring, but seems as if attached to it. The latter shades off 
toward its inner edge, and merges gradually into the dusky ring. 
The latter extends about half way from the inner edge of the bright 
ring to the ball of the planet. 

Aspect of the Rings.— As Saturn revolves around the sun, the 
plane of the rings remains parallel to itself. That is, if we consider 
a straight line passing through the centre of the planet, perpendic- 
ular to the plane of the ring, as the axis of the latter, this axis will 
always point in the same direction. In this respect the motion is 
similar to that of the earth around the sun. The ring of Saturn is 
inclined about 27° to the plane of its orbit. Consequently, as the 
planet revolves around the sun, there is a change in the direction in 
which the sun shines upon it similar to that which produces the 
change of seasons upon the earth, as shown in Fig. 32. 

The corresponding changes for Saturn are shown in Fig 76. Dur- 
ing each revolution of Saturn the plane of the ring passes through 
the sun twice. This occurred in the years 1862 and 1878, at two 
opposite points of the orbit, as shown in the figure. At two other 
points, midway between these, the sun shines upon the plane of the 
ring at its greatest inclination, about 27°. Since the earth is little 
more than one tenth as far from the sun as Saturn is, an observer 
always sees Saturn nearly, but not quite, as if he were upon the sun. 
Hence at certain times the rings of Saturn are seen edgeways; while 
at other times they are at an inclination of 27°, the aspect depending 
upon the position of the planet in its orbit. The following are the 
times of some of the phases: 

1878, February 7th. — The edge of the ring was turned toward the 
sun. It could then be seen only as a thin line of light. 

1885. — The planet having moved forward 90°, the south side of the 
rings may be seen at an inclmation of 27°. 

1891, December. — The planet having moved 90° further, the edge 
of the ring is again turned toward the sun. 

1899. — The north side of the ring is inclined toward the sun, and 
is seen at its greatest inclination. 

The rings are extremely thin in proportion to their extent. Con- 
sequently, when their edges are turned toward the earthy they appear 
as a thin line of light, which can be seen only with powerful tele- 
scopes. With such telescopes, the planet appears as if it were 



BATUBN AND ITS STSTMM. 



251 



pierced through by a piece of very fine wire, the ends of which pro- 
ject on each side more than the diameter of the planet. It has fre- 
quently been remarked that this appearance is seen on one side of 
the planet, when no trace of the ring can be seen on the other. 

There is sometimes a period of a few weeks during which the 
plane of the ring, extended outward, passes between the sun and the 
earth. That is, the sun shines on one side of the ring, while the 
other or dark side is turned toward the earth. In this case it seems 
to be established that only the edge of the ring is visible. If this be 




Fig. 76.— Different Aspects of the Ring of Saturn as seen from the 
Earth. 



so, the substance of the rings cannot be transparent to the sun's rays, 
else it would be seen by the light which passes through it. 

Constitution of the Rings of Saturn. — Tiie nature of these objects 
has been a subject both of wonder and of investigation by mathema- 
ticians and astronomers ever since they were discovered. They were 
at first supposed to be solid bodies; indeed, from their appearance it 
was difficult to conceive of them as anything else. The question 
then arose: Wliat keeps them from falling on the planet? It was 
shown by La Place that a homogeneous and solid ring surrounding 
the planet could not remain in a state of equilibrium, but must be 
precipitated upon the central ball by the smallest disturbing force. 



m^ 



ASmONOMT, 



It is now established beyond reasonable doubt that the rings do not 
form a continuous mass, but are really a countless multitude of small 
separate particles, each of which revolves on its own account. These 
satellites are individually far too small to be seen in an}'- telescope, but 
so numerous that when viewed from the distance of the earth they 
appear as a continuous mass, like particles of dust floating in a 
sunbeam. 

Satellites of Saturn. 

Outside the rings of Saturn revolve its eight satellites, the order 
and discovery of which are shown in the following table: 



No. 


Name. 




Discoverer. 


Date of Discovery. 


1 
2 
3 
4 
5 
6 
7 
8 


Mimas 

Enceladus 

Tethys 

Dione 

Rhea 

Titan 

Hyperion 

Japetus 


3-3 
4-3 
5-3 

6-8 

9-5 

20-7 

26-8 

64-4 


Herschel 

Herschel 

Cassini 

Cassini 

Cassini 

Huyii'hens 

Bond 

Cassini 


1789. September 17. 
1789, August 28. 
1684. March. 
1684, March. 
1672, December 23. 
1655, March 25. 
1848, September 16. 
1671, October. 



The distances from the planet are given in radii of the latter. The 
satellites Mimas and Hyperion are visible only in the most powerful 
telescopes. The brightest of all is Titan, which can be seen in a 
telescope of the smallest ordinar}'^ size. Japetus has the remarkable 
peculiarity of appearing nearly as bright as litan when seen west of 
the planet, and so faint as to be visible only in large telescopes when 
on tiie other side. This appearance is explained by supposing that, 
like our moon, it always presents the same face to the planet, and 
that one side of it is dark and the other side light. When west of 
the planet, the bright side is turned toward the earth and the satel- 
lite is visible. On the other side of the planet, the dark side is turned 
toward us, and it is nearly invisible. Most of the remaining five 
satellites can ordinarily be seen with telescopes of moderate power. 



CHAPTER IX. 
THE PLANET URANUS. 

Uranus was discovered on March 13Lh, 1781, by Sir 
William Herschel (then an amateur observer) with a 
tcD-foot reflector made by himself. He Avas examining a 
portion of tlie sky near H Gemiiiorum, when one of the 
stars in the field of view attracted his notice by its peculiar 
ajipearance. On further scrutiny, it proved to have a 
planetary disk, and a motion of over 2" per hour. Herschel 
at first supposed it to be a comet in a distant part of its 
oi'bit, and under this impression parabolic orbits were com- 
puted for it by various mathematicians. None of these, 
however, satisfied subsequent observations, and it was 
finally determined tbat the new body was a planet revolv- 
ing in a nearly circular orbit. We can scarcely compre- 
hend now the enthusiasm Avith which tliis discovery was 
received. No new body (save comets) had been added to 
the solar system since the discovery of the third satellite 
of Saturn in 1684, and all the major planets of the heavens 
had been known for thousands of years. 

Uranus revolves about the sun in 84 years. Its apparent 
diameter as seen from the earth varies little, being about 
3".9. Its true diameter is about 50,000 kilometres, and its 
figure is, so far as we know, exactly spherical. 

In physical appearance it is a small greenish disk with- 



%4: AsmomMT. 

out markings. It is possible that the centre of the disk is 
slightly brighter than the edges. At its nearest approach 
to the earth, it shines as a star of the sixth magnitudCj 
and is just visible to an acute eye when the attention is 
directed to its place. In small telescopes with low powers, 
its appearance is not markedly different from that of stars 
of about its own brilliancy. 

Sir William Herschel suspected that Ura7ius was ac- 
companied by six satellites. 

Of the existence of two of these satellites there has never 
been any doubt. N"one of the other four satellites de- 
scribed by Herschel has ever been seen, and he was 
undoubtedly mistaken in supposing them to exist. Two 
additional ones were discovered by Lassell in 1847, and 
they are, with the satellites of Mars, the faintest objects in 
the solar system. Neither of them is identical with any of 
the missing ones of Herschel. As Sir AVilliam Her- 
schel had suspected six satellites, the following names for 
the true satellites are generally adopted to avoid confusion: 

DAYS. 

I. Ariel Period = 2.520383 

11. Umbriel " =: 4.144181 

III. Titania, Herschel's (II. ) " = 8 . 705897 

IV. Oberon, Herschel's (I V. ) " = 13 . 463269 

It is likely that Ariel varies in brightness on different 
sides of the planet, and the same phenomenon has also 
been suspected for Titania. 

The most remarkable feature of the satellites of Uranus is that 
their orbits are uearly perpendicular to the ecliptic instead of 
having a small inclination to that plane, like those of all the orbits 
of both planets and satellites previously known. To form a correct 
idea of the position of the orbits, we must imagine them tipped over 
until their north pole is nearly 8° below the ecliptic, instead of 90° 



THE PLANET URANUS. 255 

above it. The pole of the orbit which should be considered as the 
north one is that from which, if an observer look down upon a re- 
volving body, the latter would seem to turn in a direction opposite 
that of the hands of a watch. When the orbit is tipped over more 
than a right angle, the motion from a point in the direction of the 
north pole of the ecliptic will seem to be the reverse of this; it is 
therefore sometimes considered to be retrograde. This term is fre- 
quently applied to the motion of the satellites of Uranvs, but is 
rather misleading, since the motion, being nearly perpendicular to 
the ecliptic, is not exactly expressed by the term. 

The four satellites move in the same plane. This fact renders it 
highly probable that the planet Uranus revolves on its axis in the 
same plane with the orbits of the satellites, and is therefore an oblate 
spheroid like the earth. This conclusion is founded on the consid- 
eration that if the planes of the satellites were not kept together by 
some cause, they would gradually deviate from each other owing to 
the attractive force of the sun upon the planet. The dijfferent satel- 
lites would deviate by different amounts, and it w^ould be extremely 
improbable that all the orbits would at any time be found in the 
same plane. Since we see them in the same plane, we conclude that 
some force keeps them there, and the oblateness of the planet would 
cause such a force. 



CHAPTER X. 
THE PLANET NEPTUNE. 

Aftek the planet Uranus had been observed for some 
thirty years, tables of its motion were prepared by Bou- 
VAKD. He had as data available for this purpose not only 
the observations since 1781, but also observations extend- 
ing back as far as 1695, in which the planet was observed 
and supposed to be a fixed star. As one of the chief diffi- 
culties in the way of obtaining a theory of the planet's 
motion was the short period of time during which it had 
been regularly observed, it was to be supposed that these 
ancient observations would materially aid in obtaining 
exact accordance between the theory and observation. But 
it was found that, after allowing for all perturbations pro- 
duced by the known planets, the ancient and modern 
observations, though undoubtedly referring to the same 
object, were yet not to be reconciled with each other, but 
differed systematically. Bouyard was forced to omit the 
older observations in his tables, which were published in 
1820, and to found his theory upon the modern observa- 
tions alone. By so doing, he obtained a good agreement 
between theory and the observations of the few years 
immediately succeeding 1820. 

BouvARD seems to have formulated the idea that a pos- 
sible cause for the discrepancies noted might be the exist- 
ence of an unknown planet, but the meagre data at his 
disposiil forced him to leave the subject untouched, In 



THE PLANET NEPTUNE. 257 

1830 it was found that the tables whicli represented the 
motion of the planet well in 1820-25 were 20" in error, in 
1840 the error was 90", and in 1845 it was over 120". 

These progressive and systematic changes attracted the 
attention of astronomers to the subject of the theory of 
the motion of Uramis. The actual discrepancy (120") in 
1845 was not a quantity large in itself. Two stars of the 
magnitude of Uranus, and separated by only 120", would 
be seen as one to the unaided eye. It was on account of 
its systematic and progressive increase that suspicion was 
excited. Several astronomers attacked the problem in 
various ways. The elder Struye, at Pulkova, prosecuted 
a search for a new planet along with his double-star obser- 
vations; Bessel, at Koenigsberg, set a student of his own, 
Flemiis^g, at a new comparison of observation with theory, 
in order to furnish data for a new determination; Arago, 
then Director of the Observatory at Paris, suggested this 
subject in 1845 as an interesting field of research to Le 
Verrier, then a rising mathematician and astronomer. 
Mr. J. C. Adams, a student in Cambridge University, 
England, had become aware of the problems presented by 
the anomalies in the motion of Uranus, and had attacked 
this question as early as 1843. In October, 1845, Adams 
communicated to the Astronomer Eoyal of England ele- 
ments of a new planet so situated as to produce the per- 
turbations of the motion of Uranus which had actually 
been observed. Such a prediction from an entirely un- 
known student, as Adams then was, did not carry entire 
conviction with it. A series of accidents prevented the 
unknown planet being looked for by one of the largest 
telescopes in England, and so the matter apparently 
dropped. It may be noted, however, that we now know 



258 ASTRONOMY. 

Adams' elements of the new planet to have been so near 
the truth that if it had been really looked for by the power- 
ful telescope which afterward discovered its satellite, it 
could scarcely have failed of detection. 

Bessel's pupil Fleming died before his work was done, 
and Bessel's researches were temporarily brought to an 
end. Struve's search was unsuccessful. Only Le Ver- 
RiER continued his investigations, and in the most 
thorough manner. He first computed anew the pertur- 
bation of Ura7ius produced by the. action of Jupiter and 
Saturn. Then he examined the nature of the irregulari- 
ties observed. These showed that if they were caused by 
an unknown planet, it could not be between Saturn and 
Ura7ius, or else Saturn would have been more affected 
than was the case. 

The new planet was outside of Uranus if it existed at 
all, and as a rough guide Bode's law was invoked, which 
indicated a distance about twice that of TJranus. In the 
summer of 1846 Le Verrier obtained complete elements 
of a new planet, which would account for the observed 
irregularities in the motion of Uranus, and these were 
published in France. They were very similar to those of 
Adams, which had been communicated to Professor Chal- 
LIS, the Director of the Observatory of Cambridge, Eng- 
land. 

A search was immediately begun by Challis for such 
an object, and as no star-maps were at hand for this region 
of the sky, he began mapping the surrounding stars. In 
so doing the new planet was actually observed, both on 
August 4th and 12th, 1846, but the observations remain- 
ing unreduced, and so the planetary nature of the object 
was not recognized. 



THE PLANET NEPTUNE, 



259 



In September of the same year Le Vekriee wrote to 
Dr. Galle, then Assistant at the Observatory of Berlin, 
asking him to search for the new planet, and directing 
him to the place where it should be found. By the aid 
of an excellent star-chart of this region, which had just 
been completed, the planet was found September 23d, 1846. 

The strict rights of discovery lay with Le Vereier, 
but the common consent of mankind has always credited 




Fig. 77. 

Adams with an equal share in the honor attached to this 
most brilliant achievement. Indeed, it was only by the 
most unfortunate succession of accidents that the discovery 
did not attach to Adams' researches. One thing must in 
fairness be said, and that is that the results of Le Ver- 
RiER, which were reached after a most thorough investi- 
gation of the whole ground, were announced with an en- 
tire confidence which, perhaps, was lacking in the other 
case. 



260 ASTRONOMY. 

This brilliant discoyery created more enthusiasm than 
even the discovery of Uranus, as it was by an exercise of 
far higher qualities that it was achieved. It appeared to 
savor of the marvellous that a mathematician could say 
to a working astronomer that by pointing his telescope to 
a certain small area, within it should be found a new 
major planet. Yet so it was. 

The general nature of the disturbing force which re- 
vealed the new planet may be seen by Fig. 77, which 
shows the orbits of the two planets, and their respective 
motions between 1781 and 1840. The inner orbit is that 
of Uranus, the outer one that of Neptune. The arrows 
passing from the former to the latter show the directions 
of the attractive force of Neptune. It will be seen that 
the two planets were in conjunction in the year 1822. 
Since that time Uranus has, by its more rapid motion, 
passed more than 90° beyond Neptune, and will continue 
to increase its distance from the latter until the begin- 
ning of the next century. 

Our knowledge regarding Neptune is mostly confined to 
a few numbers representing the elements of its motion. 
Its mean distance is more than 4,000,000,000 kilometres 
(2,775,000,000 miles); its periodic time is 164.78 years; 
its apparent diameter is 2.6 seconds, corresponding to a 
true diameter of 55,000 kilometres. Gravity at its surface 
is about nine tenths of the corresponding terrestrial surface 
gravity. Of its rotation and physical condition nothing 
is known. Its color is a pale greenish blue. It is attended 
by one satellite, which was discovered by Mr. Lassell, of 
England, in 1847. The satellite requires a telescope of 
twelve inches' aperture or upward to be well seen. 



CHAPTER XL 
THE PHYSICAL CONSTITUTION OF THE PLANETS. 

It is remarkable that the eight large planets of the solar 
system, considered with respect to their physical constitu- 
tion as revealed by the telescope and the spectroscope, may 
be divided into four pairs, the planets of each pair having 
a great similarity, and being quite different from the ad- 
joining pair. 

Mercury and Venus. — Passing outward from the sun, the 
first pair we encounter will be Mercury and Venus. The 
most remarkable feature of these two planets is a negative 
rather than a positive one, being the entire absence of any 
certain evidence of change on their surfaces. We have al- 
ready shown that Venus has a considerable atmosphere, 
while there is no evidence of any such atmosphere around 
Mercury, They have therefore not been proved alike in 
this respect, yet, on the other hand, they have not been 
proved different. In every other respect than this the 
similarity appears perfect. N"o permanent markings have 
ever been certainly seen on the disk of either. If, as is 
possible, the atmosphere of both planets is filled with clouds 
and vapor, no change, no openings, and no formations 
among these cloud masses are visible from the earth. When- 
ever either of these planets is in a certain position relative 
to the earth and the sun, it seemingly presents the same 
appearance, and not the slightest change occurs in that 



262 ASTRONOMY. 

appearance from the rotation of the planet on its axis, 
which every analogy of the solar system leads us to believe 
must take place. 

When studied with the spectroscope, the spectra of Mer- 
cury and Venus do not differ strikingly from that of the 
sun. This would seem to indicate that the atmospheres of 
these planets do. not exert any decided absorption upon the 
rays of light which pass through them ; or, at least, they 
absorb only the same rays which are absorbed by the at- 
mosphere of the sun and by that of the earth. The one 
point of difference is that the lines of the spectrum pro- 
duced by the absorption of our own atmosphere appear 
darker in the spectrum of Venus, If this were so, it 
would indicate that the atmosphere of Venus is similar in 
constitution to that of our earth, because it absorbs the 
same rays. But the means of measuring the darkness of 
the lines are as yet so imperfect that it is impossible to 
speak with certainty on a point like this. 

The Earth and Mars. — These planets are distinguished 
from all the others in that their visible surfaces are mark- 
ed by permanent features, which show them to be solid, 
and which can be seen from the other heavenly bodies. It 
is true that we cannot study the earth from any other 
body, but we can form a very correct idea how it would 
look if seen in this way (from the moon, for instance). 
Wherever the atmosphere was clear, the outlines of the 
continents and oceans would be visible, while they would 
be invisible where the air was cloudy. 

Now, so far as we can judge from observations made at 
so great a distance, never much less than forty millions of 
miles, the planet Mars presents to our telescopes very 
much the same general appearance that the earth would if 



PHYSICAL OONSTtTtfTION OP TEE PLANETS. 26S 

observed from an equally great distance. The only ex- 
ception is that the visible surface of Mars is seemingly much 
less obscured by clouds than that of the earth would be. In 
other words, that planet has a more sunny sky than ours. 
It is, of course, impossible to say what conditions we might 
find could we take a much closer view of Mars : all we can 
assert is, that so far as we can judge from this distance, 
its surface is like that of the earth,. 

This supposed similarity is strengthened by the spectro- 
scopic observations. 

Jupiter and Saturn. — The next pair of planets is Jupi- 
ter and Saturn. Their peculiarity is that no solid crust 
or surface is visible from without. In this respect they 
differ from the earth and Mars, and resemble Mercury 
and Venus. But they differ from the latter in the very 
important point that constant changes can be seen going 
on at their surfaces. The preponderance of evidence is 
in favor of the view that these planets have no solid 
crusts whatever, but consist of masses of molten matter, 
surrounded by envelopes of vapor constantly rising from 
the interior. 

This view is further strengthened by their very small 
specific gravity, which can be accounted for by supposing 
that the liquid interior is nothing more than a compara- 
tively small central core, and that the greater part of the 
bulk of each planet is composed of vapor of small density. 

That the visible surfaces of Jiqnter and Saturn are cov- 
ered by some kind of an atmosphere follows not only from 
the motion of the cloud forms seen there, but from the 
spectroscopic observations. 

Uranus and Neptune. — These planets have a strikingly 
similar aspect when seen through a telescope. They differ 



264 ASTRONOMY. 

from Jupiter and Saturn in that no changes or variations 
of color or aspect can be made out upon their surfaces; 
and from the earth and Mars in the absence of any perma- 
nent features. Telescopicallj, therefore, we might classify 
them with Mercury and Venus, but the spectroscope re- 
veals a constitution entirely different from that of any 
other planets. The most marked features of their spectra 
are very dark bands, evidently produced by the absorption 
of dense atmospheres. Owing to the extreme faintness of 
the light which reaches us from these distant bodies, the 
regular lines of the solar spectrum are entirely invisible in 
their spectra, yet these dark bands which are peculiar to 
them have been seen by several astronomers. 

This classification of the eight planets into pairs is ren- 
dered yet more striking by the fact that it applies to what 
we have been able to discover respecting the rotations of 
these bodies. The rotation of the inner pair, Mercury 
and Vemis, has eluded detection, notwithstanding their 
comparative proximity to us. The next pair, the earth 
and Mars, have perfectly definite times of rotation, 
because their outer surfaces consist of solid crusts, every 
part of which must rotate in the same time. The next 
pair, Jupiter and Saturn, have well-established times 
of rotation, but these times are not perfectly definite, 
because the surfaces of these planets are not solid, and dif- 
ferent portions of their mass may rotate in slightly different 
times. Jupiter and Saturn have also in common a very 
rapid rate of rotation. Finally, the outer pair, Uranus 
and Neptune, seem to be surrounded by atmospheres of 
such density that no evidence of rotation can be gathered. 
Thus it seems that of the eight planets only the central 
four have yet certainly indicated a rotation on their axes. 



CHAPTER XII. 
METEORS. 

Phenomena and Causes of Meteors. 

DuRiiira the present century evidence has been collected 
that countless masses of matter, far too small to be seen 
with the most powerful telescopes, are moving through 
the planetary spaces. This evidence is afforded by the 
phenomena of '^aerolites/' ** meteors," and '^^shooting- 
stars." Although these several phenomena have been ob- 
served and noted from time to time since the earliest his- 
toric era, it is only recently that a complete explanation 
has been reached. 

Aerolites. — Reports of the falling of large masses of 
stone or iron to the earth have been familiar to antiqua- 
rian students for many centuries. The problem where 
such a body could come from, or how it could get into the 
atmosphere to fall down again, formerly seemed so nearly 
incapable of solution that it required some credulity to 
admit the facts. When the evidence became so strong as 
to be indisputable, theories of their origin began to be 
propounded. One theory quite fashionable in the early 
part of this century was that they were thrown from 
volcanoes in the moon. This theory has little to sup- 
port it. 

The proof that aerolites did really fall to the ground first became 
conclusive by the fall being connected with other more familiar 
phenomena. Nearly every one who is at all observant of the 



266 AsmoiiOMr. 

heavens is familiar with bolides, or fire-balls-— brilliant objects having 
the appearance of rockets, which are occasionally seen moving with 
great velocity through the upper regions of the atmosphere. 
Scarcely a year passes in which such a body of extraordinary bril- 
liancy is not seen. Generally these bodies, bright though they may 
be, vanish without leaving any trace, or making themselves evident 
to any sense but that of sight. But on rare occasions their appearance 
is followed at an interval of several minutes by loud explosions like 
the discharge of a battery of artillery. The fall of these aerolites is 
always accompanied by light and sound, though the light may be 
invisible in the daytime. 

When chemical analysis was applied to aerolites, they were proved 
to be of extramundane origin, because they contained chemical 
combinations not found in terrestrial substances. It is true that they 
contained no new chemical elements, but only a combination of the 
elements which are found on the earth. These combinations are 
now so familiar to mineralogists that they can distinguish an aerolite 
from a mineral of terrestrial origin by a careful examination. One 
of the most frequent components of these bodies is iron. 

Meteors. — Although the meteors we have described are of dazzling 
brilliancy, yet they run by insensible gradations into phenomena, 
which any one can see on any clear night. The most brilliant 
meteors of all are likely to be seen by one person only two or three 
times in his life. Meteors having the appearance and brightness of 
a distant rocket may be seen several times a year. Smaller ones 
occur more frequently ; and if a careful watch be kept, it will be 
found that several of the faintest class of all, familiarly known as 
shooting-stars, can be seen on every clear night. We can draw no 
distinction between the most brilliant meteor illuminating the whole 
sky, and perhaps making a noise like thunder, and the faintest 
shooting-star, except one of degree. There seems to be every grada- 
tion between these extremes, so that all should be traced to some 
common cause. 

Cause of Meteors. — There is now no doubt that all these phenomena 
have a common origin, and that they are due to the earth encounter- 
ing innumerable small bodies in its annual course around the sun. 
The great difficulty in connecting meteors with these invisible bodies 
arises from the brilliancy and rapid disappearance of the meteors. 
The question may be asked. Why do they burn with so great an evolu- 
tion of light on reaching our atmosphere? To answer this question 
we must have recourse to the mechanical theory of heat. Heat is a 
vibratory motion in the particles of solid bodies and a progressive 
motion in those of gases. By making this motion more rapid we 



METEOm. 267 

make the bod}^ warmer. By simply blowing air against aiiy com- 
bustible body with sufficient velocity it can be set on fire, and, if 
incombustible, the body will be made red-hot and finally melted. 
Experiments to determine the degree of temperature thus produced 
have been made which show that a velocity of about 50 metres per 
second corresponds to a rise of temperature of one degree Centi- 
grade. From this the temperature due to any velocity can be readily 
calculated on the principle that the increase of temperature is pro- 
portional to the "energy" of the particles, which again is propor- 
tional to the square of the velocity. Hence a velocity of 500 metres 
per second would correspond to a rise of 100° above the actual tem- 
perature of the air, so that if the latter was at the freezing-point the 
body would be raised to the temperature of boiling water. A velocity 
of 1500 metres per second would produce a red heat. 

The earth moves around the sun with a velocity of about 30,000 
metres per second; consequently if it met a body at rest the concus- 
sion between the latter and the atmosphere would correspond to a 
temperature of more than 300,000°. This would instantly dissolve 
any known substance. 

It must be remembered that when we speak of these enormous 
temperatures, we are to consider them as potential, not actual, tem- 
peratures. We do not mean that the body is actually raised to a 
temperature of 300,000°, but only that the air acts upon it as if it 
were put into a furnace heated to this temperature; that is, it is 
rapidly destroyed by the intensity of the heat. 

This potential temperature is independent of the density of the 
medium, being the same in the rarest as in the densest atmosphere. 
But the actual effect on the body is not so great in a rare as in a 
dense atmosphere. Every one knows that he can hold his hand 
for some time in air at the temperature of boiling water. The rarer 
the air the higher the temperature the hand would bear without 
injury. In an atmosphere as rare as ours at the height of 50 miles, 
it is probable that the hand could be held for an indefinite period, 
though its temperature should be that of red-hot iron; hence the 
meteor is not consumed so rapidly as if it struck a dense atmosphere 
with planetary velocity. In the latter case it would probably dis- 
appear like a flash of lightning. 

The amount of heat evolved is measured not by that which 
would result from the combustion of the body, but by the ms viva 
(energy of motion) which the body loses in the atmosphere. The 
student of physics knows that motion, when lost, is changed into a 
definite amount of heat. If we calculate the amount of heat which 
is equivalent to the energy of motion of a pebble having a velocity 



268 ABTHONOMT. 

of 20 miles a second, we shall find it sufficient to raise about 1300 
times the pebble's weight of water from the freezing to the boiling 
point. This is many times as much heat as could result from burn- 
ing even the most combustible body. 

The detonation which sometimes accompanies the passage of 
very brilliant meteors is not caused by an explosion of the meteor, 
but by the concussion produced by its rapid motion through our at- 
mosphere. This concussion is of much the same nature as that pro- 
duced by a flash of lightning. The air is suddenly condensed in 
front of the meteor, while a vacuum is left behind it. 

The invisible bodies which produce meteors in the way just de- 
scribed have been called meteoroids. Meteoric phenomena depend 
very largely upon the nature of the meteoroids, and the direction and 
velocity with which they are moving relatively to the earth. With 
very rare exceptions, they are so small and fusible as to be entirely 
dissipated in the upper regions of the atmosphere. Even of those 
so hard and solid as to produce a brilliant light and the loudest deto- 
nation, only a small proportion reach the earth. On rare occasions 
the body is so hard and massive as to reach the eanh without being 
entirely consumed. The potential heat produced by its passage 
through the atmosphere is then all expended in melting and destroy- 
ing its outer layers, the inner nucleus remaining unchanged. When 
such a body first strikes the denser portion of the atmosphere, the 
resistance becomes so great that the body is generally broken to 
pieces. Hence we very often find not simply a single aerolite, but a 
small shower of them. 

Heights of Meteors. — Man}^ observations have been made to deter- 
mine the height at which meteors are seen. This is effected by two 
observers stationing themselves several miles apart and mapping out 
the courses of such meteors as they can observe. In the case of very 
brilliant meteors, the path is often determined with considerable pre- 
cision by the direction in which it is seen by accidental observers in 
various regions of the country over which it passes. This observa- 
tion is nothing but a simultaneous determination of the parallax of a 
meteor as seen from two stations. See Fig. 17. 

Meteors and shooting-stars commonly commence to be visible at a 
height of about 160 kilometres, or 100 statute miles. The separate 
results vary widely, but this is a rough mean of them. They 
are generally dissipated at about half this height, and therefore 
above the highest atmosphere which reflects the rays of the sun. 
From this it may be inferred that the earth's atmosphere rises to a 
height of at least 160 kilometres. This is a much greater height than 
it was formerly supposed to have. 



METEORS. 269 



Meteoric Showers. 



As already stated, the phenomena of shooting-stars may 
be seen by a careful observer on almost any clear night. 
In general, not more than three or four of them will be 
seen in an hour, and these will be so minute as hardly to 
attract notice. But they sometimes fall in such numbers 
as to present the appearance of a meteoric shower. On 
rare occasions the shower has been so striking as to fill the 
beholders with terror. The ancient and mediaeval records 
contain many accounts of these phenomena which have been 
brought to light through the researches of antiquarians. 

It has long been known that some showers of this class 
occur at an interval of about a third of a century. One 
was observed by Humboldt, on the Andes, on the night of 
November 12th, 1799, lasting from two o'clock until day- 
light. A great shower was seen in this country in 1833, 
and is well known to have struck the negroes of the 
Southern States with terror. The theory that the showers 
occur at intervals of 34 years was propounded by Olbers, 
who predicted a return of the shower in 1867. This pre- 
diction was completely fulfilled, but instead of appearing 
in the year 1867 only, it was first noticed in 1866. On the 
night of November 13th of that year a remarkable shower 
was seen in Europe, while on the corresponding night of 
the year following it was again seen in this country, and, 
in fact, was repeated for two or three years, gradually dy- 
ing away. 

The occurrence of a shower of meteors evidently shows 
that the earth encounters a swarm of meteoroids. The re- 
currence at the same time of the year, when the eart his 
in the same point of its orbit, shows that the earth meets 



270 ASTRONOMY. 

the swarm at the same point in successive years. All the 
meteoroids of the swarm must of course be moving in the 
same direction, else they would soon be widely scattered. 
This motion is connected with the radiant point, a well- 
marked feature of a meteoric shower. 

Radiant Point. — Suppose that, during a meteoric shower, we mark 
the path of each meteor on a star-map, as in the figure. If we con- 
tinue the paths backward in a straight line, we shall find that they 
all meet near one and the same point of the celestial sphere; that is, 
they move as if they all radiated from this point. The latter is, 
therefore, called the radiant point. In the figure the lines do not all 
pass accurately through the same point. This is owing to the un- 
avoidable errors made in marking out the path. 

It is found that the radiant point is always in the same position 
among the stars, wherever the observer may be situated, and that 
as the stars apparently move toward the west, the radiant point moves 
with them. 

The radiant point is due to the fact that the meteoroids which 
strike the earth during a shower are all moving in the same direc- 
tion. Their motions will all be parallel; hence when the bodies 
strike our atmosphere the paths described by them in their passage 
will all be parallel straight lines. A straight line seen by an ob- 
server at any point is projected as a great circle of the celestial 
sphere, of which the observer supposes himself to be the centre. If 
we draw a line from the observer parallel to the paths of the meteors, 
the direction of that line will represent a point of the sphere through 
which all the paths will seem to pass; this will, therefore, be the 
radiant point in a meteoric shower. 

Orbits of Meteoric Showers. — From what has just been said it will 
be seen that the position of the radiant point indicates the direction 
in which the meteoroids move relatively to the earth. If we also 
knew the velocity with which they are really moving in space, we 
could make allowance for the motion of the earth, and thus deter- 
mine the direction of their actual motion in space. It is not a diffi- 
cult problem to calculate the actual direction and velocity of the 
meteoric swarm in space. Having this direction and velocity, the 
orbit of the swarm around the sun admits of being calculated. 

Relations of Meteors and Comets. — The velocity of the 
meteoroids does not admit of being determined from obser- 



METEORS. 271 

vation. One element necessary for determining the orbits 
of these bodies is, therefore, wanting. In the case of the 




Fig. To.— Radiant Point op Meteoric Shower. 

showers of 1799, 1833, and 1866, commonly called the 
November showers, this element is given by the time of 



272 ASTRONOMY. 

revolution around the sun. Since the showers occur at 
intervals of about a third of a century, it is highly proba- 
ble this is the periodic time of the swarm around th esun. 
The periodic time being knoAvn, the velocity at any dis- 
tance from the sun admits of calculation from the theory 
of gravitation. Thus we have all the data for determining 
the real orbits of the group of meteors around the sun. 

The calculations necessary for this purpose were made 
by Le Verrier and other astronomers shortly after the 
great shower of 1866. The following was the orbit as 
given by Le Verrier : 

Period of revolution 33,25 years. 

Eccentricity of orbit 0.9044. 

Least distance from tlie sun 0.9890. 

Inclination of orbit , 165° 19'. 

Longitude of the node 51° 18'. 

Position of the perihelion (near tlie node). 

The publication of this orbit brought to the attention of 
the world an extraordinary coincidence which had never 
before been suspected. In December, 1865, a faint tele- 
scopic comet was discovered. Its orbit was calculated as 
follows : 

Period of revolution 33.18 years. 

Eccentricity of orbit 0.9054. 

Least distance from the sun 0.9765. 

Inclination of orbit 163° 42'. 

Longitude of the node 51° 26'. 

Longitude of the perihelion 42° 24'. 

The publication of the cometary orbit and that of the 
orbit of the meteoric group were made independently with- 
in a few days of each other by two astronomers, neither of 
whom had any knowledge of the work of the other. Com- 
i^aring them, the result is evident. The swarms of meteor- 



METEORS. 273 

oids which cause the Novemder shotuers move in the same 
orMt with this comet. 

The comet passed its perihelion in January, 1866. The 
most striking meteoric shower commenced in the following 
November, and was repeated during several 3-ears. It 
seems, therefore, that the meteoroids which produce these 
showers follow after Tempel's comet, moving in the same 
orbit with it. This shows a curious relation between 
comets and meteors, of which we shall speak more fully in 
the next chapter. When this fact was brought out, the 
question naturally arose whether the same thing might not 
be true of other meteoric showers. 

Other Showers of Meteors. — Although the November 
showers (which occur about November 14) are the only 
ones so brilliant as to strike the ordinary eye, it has long 
been known that there are other nights of the year (nota- 
bly August 10) in which more shooting-stars than usual 
are seen, and in which the large majority radiate from one 
point of the heavens. This shows conclusively that they 
arise from swarms of meteoroids moving together around 
the sun. 

The Zodiacal Light. — If we observe the western sky during the 
winter or spring months, about the end of the evening twilight, we 
shall see a stream of faint light, a little like the Milky Way, rising 
obliquely from the west, and directed along the ecliptic toward a 
point south-west from the zenith. This is called the zodiacal light. 
It may also be seen in the east before daylight in the morning during 
the autumn months, and has sometimes been traced all the way 
across the heavens. Its origin is still involved in obscurity, but it 
seems probable that it arises from an extremcl}'- thin cloud either of 
meteoroids or of semi-gaseous matter like that composing the tail of 
a comet, spread all around the sun inside the earth's orbit. Its 
spectrum is prol)ably that of reflected sunlight, a result which gives 
color to the theory tbjit it prises from ft ploud of meteoroids revolv- 
ing round the sun. 



CHAPTER XIII. 

COMETS. 
Aspect of Comets. 

Comets are distinguislied from the planets both by their 
aspects and their motions. They ccme into view without 
anything to herald their approach, continue in sight for a 
few weeks or months, and then gradually vanish in the 
distance. They are commonly considered as composed of 
three parts: the nucleus, the coma (or hair), and the tail. 

The nucleus of a comet is, to the naked eye, a point of 
light resembling a star or planet. Viewed in a telescope, 
it generally has a small disk, but shades off so gradually 
that it is difficult to estimate its magnitude. In large 
comets it is sometimes several hundred miles in diameter. 

The nucleus is always surrounded by a mass of foggy 
light, which is called the coma. To the naked eye the 
nucleus and coma together look like a star seen through a 
mass of thin fog, which surrounds it with a sort of halo. 
The nucleus and coma together are generally called the 
head of the comet. 

The tail of the comet is simply a continuation of the 
coma extending out to a great distance, and always di- 
rected aAvay from the sun. It has the appearance of a 
stream of milky light, which grows fainter and broader 
as it recedes from the head. Like the coma it shades off 
so gradually that it is impossible to fix any boundaries to 
it. The length of the tail varies from T or 3° to 90° or 



COMETS. 275 

more. Generally the more brilliant the head of the comet, 
tlie longer and brighter is the tail. 

The aboYe description applies to comets which can be 
plainly seen by the naked eye. Half a dozen telescopic 
comets may be discovered in a single year, while one of the 
brighter class may not be seen for ten years or more. 

When comets are studied with a telescope, it is found 
that they are subject to extraordinary changes of structure. 





Fig. 79.— Telescopic Comet without Fig. 80.— Telescopic Comet with 
A Nucleus. a Nucleus, 

To understand these changes, we must begin by saying that 
comets do not, like the planets, reyolve around the sun in 
nearly circular orbits, but always in orbits so elongated 
that the comet is visible in only a very small part of its 
course. See page 278, Fig. 82.) 

The Vaporous Envelopes. 

If a comet is very small, it may undergo no changes of aspect 
during its entire course. If it is an unusually bright one. a bow 
surrounding the nucleus on the side toward the sun will develop 
as the comet approaches the sun. This bow will gradually rise up 
and spread out on all sides, finally assuming the form of a semi- 
circle having the nucleus in its centre, or, to speak with more pre- 
cision, the form of a parabola having the nucleus near its focus. 
The two ends of this parabola will extend out further and further 
so as to form a part of the tail, and tinally be lost in it. Other bows 



276 ASTRONOMY. 

will successively form around the nucleus, all slowly rising from it 
like clouds of vapor. These distinct vaporous masses are called the 
envelopes : they shade off gradually into the coma so as to be with 
difficulty distinguished from it, and indeed maybe considered as part 
of it. These appearances are apparently caused by masses of vapor 
streaming up from tliat side of the nucleus nearest the sun, and grad- 
ually spreading around Ihe comet on each side. The form of a bow 
is not the real form of the envelopes, but only the apparent one in 
which we see them projected against the background of the sky. 
Perhaps their forms can be best imagined by supposing the sun to 
be directly above the comet, and a fountain, throwing a liquid hori- 
zontally on all sides, to be built upon that part of the comet which 
ia uppermost. Such a fountain would throw its water in the form 
of a sheet, falling on all sides of the cometic nucleus, but not touch- 




FiG. 81.— Formation of Envelopes. 

ing it. Two or three vapor surfaces of this kind are sometimes seen 
around the comet, the outer one enclosing each of the inner ones, 
but no two touching each other. 

The Physical Constitution of Comets. 

To tell exactly what a comet is, we should be able to show how all 
the phenomena it presents would follow from the properties of mat- 
ter, as we learn them at the surface of the earth. This, however, no 
one has been able to do, many of the phenomena being such as we 
should not expect from the known constitution of matter. All we 
can do, therefore, is to present the principal characteristics of comets, 
as shown by observation, and to explain what is wanting to reconcile 
these characteristics with the known properties of matter. 

In the first place, all comets which have been examined with the 
spectroscope show a spectrum composed, in part at least, of bright 
lines or bands. The positions and characters of these bands leave no 



COMETS. 277 

doubt that carbon, hydrogen, and nitrogen, and probably oxygen are 
present in the cometary matter. More than twenty comets have been 
examined since the invention of the spectroscope and all agree in 
giving the same evidence. In some recent comets sodium has also 
been discovered. 

In the last chapter it was shown that swarms of minute particles 
called meteoroids follow certain comets in their orbits. This is no 
doubt true of all comets. We can only regard these meteoroids as 
fragments or debris of the comet. On this theory a telescopic comet 
which has no nucleus is simply a cloud of these minute bodies. The 
nucleus of the brighter comets may either be a more condensed mass 
of such bodies or it may be a solid or liquid body itself. 

If the reader has any difticulty in reconciling this theory of de- 
tached particles with the view already presented, that the envelopes 
from which the tail of the comet is formed consist of layers of vapor, 
he must remember that vaporous masses, such as clouds, fog. and 
smoke, are really composed of minute separate particles of water or 
carbon. 

Formation of the Comet's Tail. — The tail of the comet is not a per- 
manent appendage, but is composed of the masses of v;ipor which 
we have already described as ascending from the nucleus, and after- 
ward moving away from the sun. Tlie tail which we see on one 
evening is not absolutely the same we saw the evening before, a por- 
tion of the latter having been dissipated, while new matter has taken 
its place, as with the stream of smoke from a steamship. The 
motion of the vaporous matter which forms the tail being always 
away from the sun, there seems to be a repulsive force exerted by 
the sun upon it. The form of the comet's tail, on the supposition 
that it is composed of matter driven away from the sun with a uni- 
formly accelerated velocity, has been several times investigated, and 
found to represent the observed form of the tail so nearly as to 
leave little doubt of its correctness. We may, therefore, regard it as 
an observed fact that the vapor which rises from the nucleus of the 
comet is repelled by the sun instead of being attracted toward it, as 
larger masses of matter are. 

No adequate explanation of this repulsive force has ever been 
given. 

Motions of Comets. 

Previous to the time of Newton, no certain knowledge respecting 
the actual motions of comets in the heavens had been acquired, ex- 
cept that they did not move around the sun in ellipses like the planets. 



278 ASTRONOMY. 

When Newton investigated the mathematical results of the theory 
of gravitation, he found that a body moving under the attraction of 
the sun might describe either of the three conic sections, the ellipse, 
parabola, or hyperbola. Bodies moving in an ellipse, as the planets, 
would complete their orbits at regular intervals of time, according 
to laws already laid down. But if the body moved in a parabola or 
an hyperbola, it would never return to the sun after once passing it, 
but would move off to infinity. It was, therefore, very natural to 
conclude that comets miglit be bodies which resemble the planets in 
moving under the sun's attraction, but which, instead of describing 




Fig. 82.— Elliptic and Parabolic Orbits. 

an ellipse in regular periods, like the planets, move in parabolic or 
hyperbolic orbits, and therefore only approach the sun a single time 
during their whole existence. 

This theory is now known to be essentially true for most of the 
observed comets. A few are indeed found to be revolving around 
the sun in elliptic orbits, which differ from those of the planets only 
in being much more eccentric. But the greater number which have 
been observed have receded from the sun in orbits which we are un- 
able to distinguish from parabolas, though it is possible they may be 
extremely elongated ellipses. Comets are therefore divided with re- 



COMETS. 279 

spcct to their motions into two classes: (1) periodic comets, which are 
known to move in elliptic orbits, and to return to the sun at fixed in- 
tervals; and (2) 'parabolic comets, apparently moving in parabolas, 
never to return. 

The first discovery of the periodicity of a comet was made by Hal- 
ley in connection with the great comet of 1682. Examining the records 
of past observations, he found that a comet moving in nearly the 
same orbit with that of 1682 had been seen in 1607, and still another 
in 1531. He was therefore led to the conclusion that these three 
comets were really one and the same object, returning to the sun at 
intervals of about 75 or 76 years. He therefore predicted that it 
would appear again about the year 1758. The comet was first seen 




Fig. 83. — Orbit of Halley's Comet. 

on Christmas-day, 1758, and passed its perihelion March 12th, 1759, 
only one month before the predicted time. At present it is possible 
to predict the places of some of the best known periodic comets 
almost as accurately as the positions of the planets. 

We give a figure showing the position of the orbit of Halley's 
comet relative to the orbits of the four outer planets. It attained its 
greatest distance from the sun, far beyond the orbit of Neptune, 
about the year 1873, and then commenced its return journey. The 
figure shows the position of the comet in 1874. It was then far be- 
yond the retich of the most powerful telescope, but its distance and 
direction admit of being calculated with so much precision that a 
telescope could be pointed at it at any required moment. 



280 ASTRONOMY. 

Remabeable Comets 

It is familiarly known that bright comets were in former 
years objects of great terror, being supposed to presage 
the fall of empires, the death of monarchs, the approach 
of earthquakes, wars, pestilence, and every other calamity 
which could afflict mankind. In showing the entire 
groundlessness of such fears, science has rendered one of 
its greatest benefits to mankind. 

In 1456 the comet known as Halley's, appearing 
when the Turks were making war on Christendom, caused 




Fig. 84.— Medal of the Great Comet of 1680-81. 

such terror that Pope Calixtus ordered prayers to be 
offered in the churches for protection against it. This 
is supposed to be the origin of the popular myth that the 
Pope once issued a bull against the comet. 

The number of comets visible to the naked eye, so far as 
recorded, has generally ranged from twenty to forty in a 
century. Only a small portion of these, however, have 
been so bright as to excite universal notice. 

Comet of 1680. — One of the most remarkable of these 
brilliant comets is that of 1680. It insi)ired such terror 
that a medal, of which we present a figure, was struck 
upon the Continent of Europe to quiet apprehension. A 
free translation of the inscription is : '' The star threatens 



COMETS. 381 

evil things ; trust only ! God will turn tliem to good." * 
What makes this comet especially remarkable in history 
Is that Newtok calculated its orbit, and showed that it 
moved around the sun in a conic section, in obedience to 
the law of gravitation. 

Great Comet of 1811. — It has a period of over 3000 
years, and its aphelion distance is about 40,000,000,000 
miles. 

Great Comet of 1843. — One of the most brilliant comets 
which have appeared during the present century was that 
of February, 1843. It was visible in full daylight close to 
the sun. Considerable terror was caused in some quar- 
ters lest it might presage the end of the world, which had 
been predicted for that year by Miller. At perihelion it 
passed nearer the sun than any other body has ever been 
known to pass, the least distance being only about one 
fifth of the sun's semidiameter. With a very slight 
change of its original motion, it would have actually fallen 
into the sun. 

Great Comet of 1858. — Another comet remarkable for 
the length of time it remained visible w\as that of 1858. 
It is frequently called after the name of Donati, its first 
discoverer. No comet visiting our neighborhood in recent 
times has afforded so favorable an opportunity for study- 
ing its physical constitution. Its greatest brilliancy 
occurred about the beginning of October, when its tail was 
40° in length and 10° in breadth at its outer end. Its period 
is 1950 years. 

* The student slionld notice the care which the nuthor of the in- 
scription has taken to make it consolatory, to make it rhyme, and 
to give implicitly the year of the comet by writing certain Roman 
numerals hirger than the other letters. 




Fig. 85.— Donati's Comet or 1858. 



COMETS. 283 

Great Comet of 1882. — It is yet too soon to speak of the 
results of the observations on this magnificent object. Its 
splendor will not soon be forgotten by those who have 
seen it. 

Encke's Comet and the Kesisting Medium. — Of telescopic comets, 
that which has been most investigated by astronomers is known as 
Encke's comet. Its period is between three and four years. Viewed 
with a telescope, it is not different in any respect from other tele- 
scopic comets, appearing simply as a mass of foggy light, somewhat 
brighter near one side. Under the most favorable circumstances, it 
is just visible to the naked eye. The circumstance which has lent 
most interest to this comet is that the observations which have been 
made upon it seem to indicate that it is gradually approaching tho 
sun. Encke attributed this change in its orbit to the existence in 
space of a resisting medium, so rare as to have no appreciable effect 
upon the motion of the planets, and to be felt only by bodies of ex- 
tieme tenuity, like the telescopic comets. The approach of the 
comet to the sun is shown, not by direct observation, but only by a 
gradual diminution of the period of revolution. It will be many 
centuries before thif period would be so far diminished that the 
comet would actually touch the sun. 

If the change in the period of this comet were actually due to the 
cause wliicli Encke supposed, then other faint comets of the same 
kind ought to be subject to a similar influence. But the investiga- 
tions which have been made in recent times on these bodies show no 
deviation of the kind. It might, therefore, be concluded that the 
change in the period of Encke's comet must be due to some other 
cause. There is, however, one circumstance which leaves us in 
doubt. Encke's comet passes nearer the sun than any other comet 
of short period which has been observed with sufficient care to de- 
cide the question. It may, therefore, be supposed that the resisting 
medium, wiiatever it may be, is densest near the sun, and does not 
extend out far enough for the other comets to meet it. The question 
is one very difficult to settle. The fact is that all comets exhibit 
slight anomalies in their motions which prevent us from deducing 
conclusions from them with the same certainty that we should from 
those of the planets. One of the chief difficulties in investigating 
the orbits of comets with all rigor is due to the difficulty of obtaining 
accurate positions of the centre of so ill-defined an object as the 
nucleus. 



PART III. 

THE UNIVERSE AT LARGE. 



INTRODUCTIOK 



Ik our studies of the heavenly bodies, we have hitherto 
been occupied almost entirely with those of the solar sys- 
tem. Although this system comprises the bodies which 
are most important to us, yet they form only an insignifi- 
cant part of creation. Besides the earth on which we 
dwell, only seven of the bodies of the solar system are 
plainly visible to the naked eye, whereas some 2000 stars 
or more can be seen on any clear niglit. 

The material universe, as revealed by the telescope, con- 
sists principally of shining bodies, many millions in num- 
ber, a few of the nearest and brightest of which are visible 
to the naked eye as stars. They extend out as far as the 
most powerful telescope can penetrate, and no one knows 
how much farther. Our sun is simply one of these stars, 
and does not, so far as we know, differ from its fellows in any 
essential characteristic. From the most careful estimates, 
it is rather less bright than the average of the nearer stars, 
and overpowers them by its brilliancy only because it is so 
much nearer to us. 

The distance of the stars from each other, and therefore 
from the sun, is immensely greater than any of the dis- 
tances which we have hitherto had to consider in the solar 



286 ASTRONOMY. 

system. In fact, the nearest known star is about seven 
thousand times as far as the planet Neptune. If we sup- 
pose the orbit of this planet to be represented by a child's 
hoop, the nearest star would be three or four miles away. 
We have no reason to suppose that contiguous stars are, on 
the average, nearer than this, except in special cases where 
they are collected together in clusters. 

The total number of the stars is estimated by millions, and 
they are probably separated by these wide intervals. It 
follows that, ingoing from the sun to the nearest star, we 
would be simply taking one step in the universe. The 
most distant stars visible in great telescopes are probably 
several thousand times more distant than the nearest one, 
and we do not know Avhat may lie beyond. 

The point we wish principally to impress on tlic reader 
in this connection is that, although the stars and planets pi'c- 
sent to the naked eye so great a similarity in appearance, 
there is the greatest possible diversity in their distances 
and characters. The planets, though many millions of 
miles away, are comparatively near us, and form a little 
family by themselves, which is called the solar system. 
The fixed stars are at distances incomparably greater — the 
nearest star being thousands of times more distant than 
the farthest planet. The planets are, so far as we can see, 
worlds somewhat like this on which we live, while the stars 
are suns, generally larger and brighter than our own. 
Each star may, for aught we know, have planets revolving 
around it, but their distance is so immense that the largest 
planets will remain invisible with the most powerful tele- 
scopes man can ever hope to construct. 

The classification of the heavenly bodies thus leads us to 
this curious conclusion. Our sun is one of the family of 



THE UNIVERSE AT LARGE. 287 

stars, tlie other members of which stud the heavens at 
night, or, in other words, the stars are suns like that which 
makes the day. The planets, though they look like stars, 
are not such, but bodies more like the earth. 

The great universe of stars, including the creation in its 
largest extent, is called the stellar system, or stellar 
U7iiverse. We have first to consider how it looks to the 
naked eye. 



CHAPTER I. 
CONSTELLATIONS. 

General Aspect of the Heavens. 

Whei^ we view the heavens with the unassisted eje^ the 
stars appear to be scattered nearly at random over the 
surface of the celestial vault. The only deviation from an 
entirely random distribution which can be noticed is a cer- 
tain grouping of the brighter ones into constellations. 
A few stars arc comparatively much brighter than the rest, 
and there is every gradation of brilliancy, from that of 
the brightest to those which are barely visible. We also 
notice at a glance that the fainter stars outnumber the 
bright ones; so that if we divide the stars into classes ac- 
cording to their brilliancy, the fainter classes will contain 
the most stars. 

The total number one can see will depend very largely 
npon the clearness of the atmosphere and the keenness of 
the eye. There are in the whole celestial sphere about 
6000 stars visible to an ordinarily good eye. Of these, 
however, we can never see more than a fraction at any 
one time, because one half of the sphere is always below the 
horizon. If we could see a star in the horizon as easily as 
in the zenith, one half of the whole number, or 3000, would 
be visible on any clear night. But stars near the horizon 
are seen through so great a thickness of atmosphere as 
greatly to obscure their light ; consequently only the 



CONSTELLATIONS. 289 

brightest ones can there be seen. As a result of this ob- 
scuration, it is not likely that more than 2000 stars can 
ever be taken in at a single view by any ordinary eye. 
About 2000 other stars are so near the south pole 
that they never rise in our latitudes. Hence out of the 
6000 supposed to be visible, only 4000 ever come within 
the range of our vision, unless we make a journey toward 
the equator. 

The Galaxy. — Another feature of the heavens, which is 
less striking than the stars, but has been noticed from 
the earliest times, is the Galaxy, or Milky Way. This 
object consists of a mngnificcnt slream or belt of white 
milky light 10° or 15° in brcudlh, extending obliquely 
around the celestial sphere. During the sju-ing months it 
nearly coincides wiih oui- horizon in the early evening, 
but it can readily be seen at all other times of the year 
spanning the heavens like an arch. It is for a portion of 
its length split longitudinally into two parts, which remain 
separate through many degrees, and are finally united 
again. The student will obtain a better idea of it by 
actual examination than from any description. He will 
see that its irregularities of form and lustre are such that 
in some places it looks like a mass of brilliant clouds. 

Lucid and Telescopic Stars. — When we view the heavens 
with a telescope, we find that there are innumerable stars 
too small to be seen by the naked eye. We may there- 
fore divide the stars, with respect to brightness, into two 
great classes. 

Lucid Stars are those which are visible without a tele- 
scope. 

Telescopic Stars are those which are not so visible. 

When Galilbo first directed, his telescope to the heav- 



290 ASTRONOMY. 

ens, about the year 1610, he perceived that the Milky 
Way was composed of stars too faint to be individually 
seen by the unaided eye. We thus liave the interesting 
fact that although telescopic stars cannot be seen one by 
one, yet in the region of the Milky Way they are so namer- 
ous that they shine in masses like brilliant clouds. Huy- 
GHENS in 1656 resolved a large portion of the Galaxy into 
stars, and concluded that it was composed entirely of them. 
Keplek considered it to be a vast ring of stars surround 
ing the solar system, and remarked that the sun must be 
situated near the centre of the ring. This view agrees 
very well with the one now received, only that the stars 
which form the Milky Way, instead of lying around the 
solar s^^stem, are at a distance so vast as to elude all our 
powers of calculation. 

Such are in brief the more salient phenomena which 
are presented to an observer of the starry heavens. We 
shall now consider how these phenomena have been clas- 
sified by an arrangement of the stars according to their 
brilliancy and their situation. 

Magnitudes of the Stars. 

In ancient times the stars were arbitrarily classified into six 
orders of magnitude. The fourteen brightest visible in our lati- 
tude were designated as of the first magnitude, while those which 
were barely visible to the naked eye were said to be of the sixth 
magnitude. This classification, it will be noticed, is entirely arbi- 
trary, since there are no two stars which are absolutely of the same 
brightness; that is, if all the stars were arranged in the order of 
their actual brilliancy, we should find a regular gradation from the 
brightest to the faintest, no two being precisely the same. There- 
fore the brightest star of any one magnitude is about of the same 
brilliancy with the faintest one of the next higher magnitude. Be- 
tween the north pole and 35° south declination there are: 



CONSTELLATIONS. 291 

14 stars of the first magnitude. 



48 " 


" second 


153 " 


" third 


313 " 


" fourth 


854 " 


" fifth 


3974 " 


" sixth 



5355 of the first six magnitudes. 

Of these, however, nearly 2000 of the sixth magnitude are so faint 
that they can be seen only by an eye of extraordinary keenness. A 
star of the second magnitude is four tenths as bright as one of the 
first; one of the third is four tenths as bright as one of the second, 
and so on. 

The Constellations and Names of the Stars. 

The earliest astronomers divided the stars into groups, 
called constellations, and gave special proper names both 
to these groups and to many of the more conspicuous 
stars. 

"We have evidence that more than 8000 years before the commence- 
ment of the Christian chronology the star Sirius, the brightest in the 
heavens, was known to the Egyptians under the name of Sothis. 
The seven stars of the Oreat Bear, so conspicuous in our northern 
sky, were known under that name to Homer and Hesiod, as well as 
the group of the Pleiades, or Seven Stars, and the constellation of 
Orion. Indeed, it would seem that all the earlier civilized nations, 
Egyptians, Chinese, Greeks, and Hindoos, had some arbitrary divi- 
sion of the surface of the heavens into irregular and often fantastic 
shapes, which were distinguished by names. 

In early times the names of heroes and animals were given to the 
constellations, and these designations have come down to the present 
day. Each object was supposed to be painted on the surface of the 
heavens, and the stars were designated by their position upon some 
portion of the object. The ancient and mediaeval astronomers would 
speak of "the bright star in the left foot of Orion," " the eye of the 
Bull," "the heart of the Lion," "the head of Perseus" etc. These 
figures are still retained upon some star-charts, and are useful where 
it is desired to compare the older descriptions of the constellations 
with our modern maps. Otherwise they have ceased to serve any 



292 ASTRONOMY. 

purpose, and are not generally found ou maps designed for purely 
astronomical uses. 

The Arabians, who used this clumsy way of designating stars, 
gave special names to a large number of the brighter ones. Some of 
these names are in common use at the present time, as Aldeharan, 
Fomalhaut, etc. 

In 1654 Bayer, of Germany, mapped down the constellations 
upon charts, designating the brighter stars of each constellation by 
the letters of the Greek alphabet. When this alphabet was exhaust- 
ed he introduced the letters of the Roman alphabet. In general, the 
brightest star was designated by the first letter of the alphabet, a, 
the next by the following letter, (5, etc. 

On this system, a star is designated by a certain Greek letter, fol- 
lowed by the genitive of the Latin name of the coustelhition to which 
it belongs. For example, a Canis Majoris, or, in English, a of the 
Great Dog, is the designation of Sirius, the brightest star in the 
heavens. The seven stars of the Great Bear are called a UrscB itla- 
joris, (i Ursce Majoris, etc. Arcturus is a Bootis. The reader will 
liere see a resemblance to our way of designating individuals by a 
Christian name followed by the family name. The Greek letters 
furnish the Christian names of the separate stars, while the name of 
the constellation is that of the family. As there are only M\j letters 
in the two alphabets used by Bayer, it will be seen that only the 
fifty brightest stars in each constellation could be designated by this 
method. 

When by the aid of the telescope many more stars than these were 
laid down, some other method of denoting them became necessary. 
Flamsteed, who observed before and after 1700, prepared an ex- 
tensive catalogue of stars, in which those of each constellation were 
designated by numbei's in the order of right ascension. These num- 
bers were entirely independent of the designations of Bayer — that 
is, he did not omit the Bayer stars from his system of numbers, but 
numbered them as if they had no Greek letter. Hence those stars to 
which Bayer applied letters have two designations, the number and 
the letter. The fainter stars are designated either by their R.A. and 
8, or by their numbers in some catalogue of stars. 

Numbering and Cataloguing the Stars. 

As telescopic power is increased, we still find stars of fainter and 
fainter light. But the number cannot go on increasing forever in 
the same ratio as with the brighter magnitudes, because, if it did, 
the whole sky would be a blaze of starlight. 



CONSTELLATIONS. 293 

If telescopes with powers far exceeding our present ones were 
made, they would no doubt show new stars of the 20th and 21st 
magnitudes. But it is highly probable that the number of such suc- 
cessive orders of stars would not increase in the same ratio as is ob- 
served in the 8th, 9th, and 10th magnitudes, for example. The 
enormous labor of estimating the number of stars of such classes will 
long prevent the accumulation of statistics on this question; but this 
much is certain, that in special regions of the sky, which have been 
searchingly examined by various telescopes of successively increas- 
ing apertures, the number of new stars found is by no means in pro- 
portion to the increased instrumental power. If this is found to be 
true elsewhere, the conclusion may be that, after all, the stellar sys- 
tem can be experimentally shown to be of finite extent, and to con- 
tain only a finite number of stars. 

We have already stated that in the whole sky an eye of average 
power will see about 6000 stars. With a telescope this number is 
greatly increased, and the most powerful telescopes of modern times 
will probably show more than 20,000,000 stars. As no trustworthy 
estimate has ever been made, there is great uncertainty upon this 
point, and the actual number may range anywhere between 
15,000,000 and 40,000,000. Of this number, not one out of twenty 
has ever been catalogued at all. 

The southern sky has many more stars of the first seven magni- 
tudes than the northern, and the zones immediately north and south 
of the equator, although greater in surface than any others of the 
same width in declination, are absolutely poorer in such stars. 

This will be much better understood by consulting the graphical 
representation on page 294. On this chart ai-e laid down all the stars 
of the British Association Catalogue (a dot for each star), and beside 
these the Milky Way is represented. The relative richness of the 
various zones can be at once seen. 

The distribution and number of the brighter stars (1st to 7th magni- 
tude) can be well understood from this chart. 

In Argelander's Durchmufiteriwg of the stars of the northern 
heavens there are recorded as belonging to the northern hemisphere: 



10 stars betw^een the 1.0 magnitude and the 1.9 magnitude. 



128 

310 

1,016 

4,338 

13,593 

57,960 

237,544 



2.0 


2.9 


3.0 


3.9 


4.0 


4.9 


5.0 


5.9 


6.0 


6.9 


7.0 


7.9 


8.0 


8.9 


9.0 


9,5 



294 



ASTRONOMY. 




t)0N8tELLATl0N§. ggg 

In all 314,926 stars from the first to the 9.5 magnitudes are enu- 
merated in the northern sky, so that there are about 600,000 in the 
whole heavens. 

We may readily compute the amount of light received by the earth 
on a clear but moonless night from these stars. Let us assume that 
the brightness of an average star of the first magnitude is about 0.5 
of that of a LyrcB. A star of the 2d magnitude will shine with a 
light expressed by 0.5 X 0.4. = 0.20, and so on. (See p. 291.) 

The total brightness of 10 1st magnitude stars is 5.0 



10 


1st 


87 


2d 


122 


3d 


310 


4th 


1,016 


5th 


4,322 


6th 


13,593 


7th 


57,960 


8th 





7.4 




10.1 




9.9 




13.0 




22.1 




27.8 




47.4 


Sum = 


= 142.7 



It thus appears that from the stars to the 8th magnitude, inclusive, 
we receive 143 limes as much light as from a Lyrm. a Lyros has 
been determined by Zollner to be about 44,000,000,000 times faiuter 
than the sun, so that the proportion of starlight to sunlight can be 
computed. It also appears that the stars of magnitudes too high to 
allow them to be iudividually visible to the naked eye are yet so 
numerous as to affect the general brightness of the sky more than 
the so-called lucid stars (1st to 0th magnitude). The sum of the last 
two numbers of the table is greater than the sum of all the others. 

Note. — The individual stars and constellations can be 
better learned by the student from a Star Atlas than by any 
maps which can be given on a page so small as these. 



CHAPTER IL 
VARIABLE AND TEMPORARY STARS. 

Staes Regularly Variable. 

All stars do not shine with a constant light. Since the 
middle of the seventeenth century, stars variable in bril- 
liancy have been known. The period of a variable star 
means the interval of time in which it goes through all its 
changes, and returns to its original brilliancy. 

The most noted variable stars are Mir a Ceti (o Ceti) and 
Algol (/3 Persei). Mir a appears about twelve times in 
eleven years, and remains at its greatest brightness (some- 
times as high as the 2d magnitude, sometimes not above 
the 4th) for some time, then gradually decreases for about 
74 days, until it becomes invisible to the naked eye, and so 
remains for about five or six months. From the time of 
its reappearance as a lucid star till the time of its maximum 
is about 43 days. The inean period, or the interval from 
minimum to minimum, is about 333 days, but this period 
varies greatly. The brilliancy of the star at the maxima 
also varies. 

Algol has been known as a variable star since 1667. 
This star is commonly of the 2d magnitude; after remain- 
ing so about 2| days, it falls to 4"" in the short time of 
4^ hours, and remains of 4''' for 20 minutes. It then com- 



VARIABLE AND TEMPORARY STARS. $97 

mences to increase in brilliancy, and in another 3t hours it 
is again of the 2d magnitude, at wliich point it remains for 
the rest of its period, about 2^ 12^. 

These two examples of the class of variable stars give a 
rough idea of the extraordinary nature of tlie phenomena 
they present. A closer examination of others discloses 
minor variations of great complexity and apparently with- 
out law. 

About 90 variable stars are well known, and as many 
more are suspected to vary. In nearly all cases the mean 
period can be fairly well determined, though anomalies of 
various kinds frequently appear. The principal anomalies 
are: 

First. The period is seldom constant. For some stars 
the changes of the period seem to follow a regular law; for 
others no law can be fixed. 

Second. The time from a minimum to the next maxi- 
mum is usually shorter than from this maximum to the 
next minimum. 

Third. Some stars (as (3 Lyrce) have not only one maxi- 
mum between two consecutive principal minima, but two 
such maxima. For (3 Lyrce, according to Argelander, 
3"* 2'' after the principal minimum comes the first maxi- 
mum; then, 3"^ 7^ after this, a secondary minimum in which 
the star is by no means so faint as in the principal mini- 
mum, and finally 3^ 3^ afterward comes the principal maxi- 
mum, the whole period being 12*^ 21^ 47°^. 



The course of one period is illustrated in the following table, 
supposing the period to begin at 0*^ 0*^. Opposite each phase is 
given the intensity of light in terms of y Lyrce, = 1. 



298 



Asi^nomuT. 



Phases of p Lyrae. 


Relative 
Intensity. 


Principal Minimum 

First Maximum 


0^ 

d^ 


0^ 
2'' 

12'' 
22'" 


0.40 
0.83 


{Second Minimum 


6*^ 


58 


Principal Maximum 


Q'^ 


0.89 


Principal Minimum 


12<i 


0.40 









The periods of 94 well-determined variable stars beins 
it appears that they are as follows: 



tabulated, 



Period between 


No. of Stars. 

13 

1 

4 

4 

5 

9 
14 
18 


Period between 


No. of Stara 


1 d. and 20 d. 
20 50 
50 100 
100 150 
150 200 
200 250 
250 300 
300 350 


350 d. and 400 d. 
400 450 
450 500 
500 550 
550 600 
600 650 
650 700 
700 750 


13 
8 
3 



1 



1 




3 = 94 



It is natural that there should be few known variables of periods 
of 500 days and over, but it is not a little remarkable that the periods 
of over hall of these variables should fall between 250 and 450 days. 

The color of over 80 per cent of the variable stars is red or orange. 
Red stars (of which 600 to 700 are known) are now receiving close 
attention, as there is a strong likeliliood of finding among them many 
new variables. 

The spectra of variable stars show changes which appear to be 
connected with the variations in their liuht. 



Temporary or New Stars. 

There are a few cases known of apparently jwic stars which have 
suddenly appeared, attained more or less brightness, and slowly de- 
creased in magnitude, either disappearing totally, or finally remain- 
ing as comparatively faint objects. 

The most famous one was that of 1572, which attained a brightness 



VAnUSLS Al^D fSlMPORART ST Am. §9^ 

greater than that of Sirius or Jupiter and approached to Venus, being 
even visible to the eye in daylight. Tycho Brake first observed this 
star in November, 1572, and watched its gradual increase in light 
until its maximum in December. It then began to diminish in bright- 
ness, and in January, 1573, it was fainter than Jupiter. In February 
it was of the 1st magnitude, in April of the 2d, in July of the 3d, and 
in October of the 4th. It continued to diminish until March, 1574, 
when it became invisible, as the telescope was not then in use. Its 
color, at first intense white, decreased through yellow and red. 
When it arrived at the 5th magnitude its color again became white, 
and so remained till its disappearance. Tycho measured its distance 
carefully from nine stars near it, and near its place there is now a star 
of the 10th or 11th magnitude, which is possibly the same star. 

The history of temporary stars is in general similar to that of the 
star of 1572, except that none have attained so great a degree of bril- 
liancy. More than a score of such objects are known to have ap- 
peared, many of them before the making of accurate observations, 
and the conclusion is probable that many have appeared without 
recognition. Among telescopic stars there is but a small chance of 
detecting a new or temporary star. 

Several supposed cases of the disappearance of stars exist, but here 
there are so many possible sources of error that great caution is neces- 
sary in admitting them. 

Two temporar}^ stars have appeared since the invention of the spec- 
troscope (1859), and the conclusions drawn from a study of their spec- 
tra are most important as throwing light upon the phenomena of 
variable stars in general. 

The general theory of variable stars which has now the most evi- 
dence in its favor is this: These bodies are, from some general cause 
not fully understood, subject to eruptions of glowing hydrogen gas 
from their interior, and to the formation of dark spots on their sur- 
faces. These eruptions and formations have in most cases a greater 
or less tendeuc}^ to a regular period. 

In the case of our sun (which is a variable star) the period is 11 
years, but in the case of many of the stars it is much shorter. Ordi- 
narily, as in the case of the sun and of a large majority of the stars, 
the variations are too slight to affect the total quantity of light to any 
visible extent. But in the case of the variable stars this spot-producing 
power and the liability to eruptions are very much greater, and thus 
we have changes of light which can be readily perceived b}' the eye. 
Some additional strength is given to this theory by the fact just men- 
tioned, that so large a proportion of the variable stars are red. It is well 
known that glowing bodies emit a larger proportion of red rays and 



goo AsTnONOMT. 

a smaller proportion of blue ones the cooler they become. It is tberiS' 
fore probable that the red stars have the least heat. This being the 
case, it is more easy to produce spots on their surface; and if their 
outside surface is so cool as to become solid, the glowing hydrogen 
from the interior when it did burst through would do so with more 
power than if the surrounding shell were liquid or gaseous. 

There is, however, at least one star of which the variations may be 
due to an entirely different cause; namely, Algol. The extreme regu- 
larity with which the light of this object fades aw\iy and disappears 
suggest.s the possibility that a dark body may be revolving around it, 
and partially eclipsing it at every revolution. The law of variation 
of its light is so different from that of the light of other variable stars 
as to suggest a different cause. Most others are near their maximum 
for only a small part of their period, while Algol is at its maximum 
for nine tenths of it. Others are subject to nearly continuous changes, 
while the light of Algol remains constant during nine tenths of its 
period. 



CHAPTER III. 
MULTIPLE STARS. 

Character of Double and Multiple Stars. 

When" we examine tlie heavens with telescopes, we find 
many cases in which two or more stars are extremely close 
together, so as to form a pair, a triplet, or a group. It is 
evident that there are two ways to account for this appear- 
ance. 

1. We may suppose that the stars happen to lie nearly 
in the same straight line from us, but have no connection 
with each other. It is evident that in this case a pair of 
stars might appear double, although the one was hundreds 
or thousands of times farther off than the other. It is, 
moreover, impossible, from mere inspection, to determine 
which is the farther off. 

2. We may suppose that the stars are really near together, 
as they appear, and are to be considered as forming a con- 
nected pair or group. 

A couple of stars in the first case is said to be optically 
double. 

Stars which are really physically connected are said to be 
'physically double. 

If the lucid stars are equally distributed over the celestial sphere, 
the chances are 80 to 1 against an}^ two being within three minutes 
of each other, and the chances are 500,000 to 1 against the six visible 
stars of the Pleiades being accidentally associated as we see them. 
When the millions of telescopic stars are considered, there is a greater 



30^ 



ASmONOMT. 




probability of such accidental juxtaposition. But the probability of 
many such cases occurring is so extremely small that astronomers 
regard all the closest pairs as physically connected. Of the 600,000 
stars of the first ten magnitudes, about 10,000, or one out of every 
60, has a companion within a distance of 30" of arc. This proportion 

is many times greater than could possi- 
bly be the result of chance distribution. 
There are several cases of stars which 
appear double to the naked eye. s LyroB 
is such a star and is an interesting ob- 
ject, from the fact that each of the two 
stars which compose it is itself double. 
This minute pair of points, capable of 
being distinguished as double only by 
the most perfect eye (without the tele- 
scope), is really composed of two pairs 
Fia. 86.-THE QTTADRxrPLE Star of stars wide apart, with a group of 
« Lyr^. smaller stars between and around 

them. The figure shows the appearance in a telescope of consider- 
able power. 

Revolutions of Double Stars— Binary Systems.— It is evident that if 
double stars are endowed with the property of mutual gravitation, 
they must be revolving around 
each other, as the earth and 
planets revolve around the sun, 
else they would be drawn to- 
gether as a single star. 

The method of determining 
the period of revolution of a 
binary star is illustrated by the 
figure, which is supposed to rep- 
resent the field of view of an in- 
verting telescope pointed toward 
the south. The arrow shows the 
direction of the apparent diur- 
nal motion. Tlie telescope is 
supposed to be so pointed that 
the brighter star may be in the 
centre of the field. The num- 
bers around the surrounding 
circle then show the angle of 

position, supposing the smaller star to be in the direction of the 
number. 




Fig. 87. 



-Position-Angle op 
Star. 



Double 



MULTIPLE STARS. 303 

Fig. 87 is an example of a pair of stars in which the position- 
angle is about 44°. 

If, by measures of tliis sort extending through a series of years, the 
distance or position-angle of a pair of stars is found to change peri- 
odically, it shows that one star is revolving around the other. Such 
a pair is called a binary star or binary system. The only distinction 
which we can make between binary systems and ordinary double 
stars is founded on the presence or absence of this observed motion. 
It is probable that nearly all the very close double stars are really 
binary systems, but that many hundreds of years are required to per- 
form a revolution in some instances, so that the motion has not yet 
been detected. 

The discovery of binary systems is one of great scientific interest, 
because from them we learn that the law of gravitation includes the 
stars as well as the solar system in its scope, and may thus be regarded 
as truly universal. 



CHAPTER lY. 

NEBULA AND CLUSTERS. 

Discovery of Nebula. 

In the star-catalogues of Ptolemy, Hevelius, and the 
earlier writers, there was included a class of nebulous or 
cloudy stars, which were in reality star-clusters. They ap- 
peared to the naked eye as masses of soft diffused light of 
greater or less extent. In this respect they were quite 
analogous to the Milky Way. In the telescope, the nebu- 
lous appearance of these spots vanishes, and they are seen 
to consist of clusters of stars. 

As the telescope was improved, great numbers of such 
patches of light were found, some of which could be re- 
solved into stars, while others could not. The latter were 
called nehulcB and the former star-clusters. 

About 1656 HuYGHENS described the great nebula of 
Ormi, one of the most remarkable and brilliant of these 
objects. During the last century Messier, of Paris, made 
a list of 103 northern nebulae, and Lacaille noted a few 
of those of the southern sky. Sir Wllliam Herschel 
with his great telescopes first gave proof of the enormous 
number of these masses. In 1786 he published a catalogue 
of one thousand new nebulae and clusters. This was fol- 
lowed in 1789 by a catalogue of a second thousand, and in 
1802 by a third catalogue of five hundred new objects of 
this class. Sir JoHi^ Herschel added about two thou- 



NEBULA AND CLUSTERS. 305 

sand more nebulae. The general catalogue of nebulae and 
clusters of stars of the latter astronomer, published in 
1864, contains 5079 nebulae. Over two thirds of these 
were first discovered by the Herschels. 

Classification of Nebuljs and Clusters. 

In studying these objects, the first question we meet is this: Are 
all these bodies chisters of stars which look diffused only because 
they are so distant that our telescopes cannot distinguish them sepa- 
rately? or are some of them in reality what they seem to be; namely, 
diffused masses of matter? 

In his early memoirs of 1784 and 1785, Sir William Herschel 
took tlie first view. He considered the Milky "Way as nothing but a 
congeries of stars, and all nebulae naturally seemed to him to be but 
stellar clusters, so distant as to cause the individual stars to disap- 
pear in a general milkiness or nebulosity. 

In 1791, however, his views underwent a change. He had dis- 
covered a nebulous star (properly so called), or a star which was un- 
doubtedly similar to the surrounding stars, and which was encom- 
passed by a halo of nebulous light. 

He says: "Nebulae can be selected so that an insensible gradation 
shall take place from a coarse cluster like the Pleiades down to a 
milky nebulosity like that in Orion, every intermediate step being 
represented. This tends to confirm the hypothesis that all are com- 
posed of stars more or less remote. 

" A comparison of the two extremes of the series, as a coarse cluster 
and a nebulous star, indicates, however, that the nebulosity about the 
star is not of a starry nature. 

•' Considering a typical nebulous star, and supposing the nucleus 
and chevelure to be connected, we may, first, suppose the whole 
to be of stars, in which case either the nucleus is enormously 
larger than other stars of its stellar magnitude, or the envelope is 
composed of stars indefinitely small; or, second, we must admit that 
the star is involved in a .shining fluid of a nature totally unTcnown to 
us. 

"The shining fluid might exist independently of stars. The 
light of this fluid is no kind of reflection from the star in the 
centre. If this matter is self-luminous, it seems more fit to pro- 
duce a star by its condensation than to depend on the star for its 
existence. 



306 



ASTRONOMY. 



"Both diffused nebulosities and planetary nebulae are better ac- 
counted for by the hypothesis of a shining fluid than by supposing 
them to be distant stars." 

This was the first exact statement of the idea that, beside stars 
and star-clusters, we have in the universe a totally distinct series of 
objects, probably much more simple in their constitution. Observa- 
tions on the spectra of these bodies have entirely confirmed the con- 
clusions of Herschel. 

Nebulae and clusters were divided by Herschel into classes. He 




Fig. 88.— Spiral Nebttia. 

applied the name planetary nebulcB to certain circular or elliptic 
nebulae which in his telescope presented disks like the planets. 
Spiral nebulm are those whose convolutions have a spiral shape. This 
class is quite numerous. 

The different kinds of nebulae and clusters will be belter under- 
stood from the cuts and descriptions which follow than by formal 
definitions. It must be remembered that there is an almost infinite 
variety of such shapes. 



l^BBULJBJ AND VLmTEJRS, 



307 






Fia. 89.--TaE OMEe^A or Horseshoe Nebula,. 



308 



ASTRONOMY. 



Star-Clustees. 

The most noted of all the clusters is the Pleiades, which have al- 
ready been briefly described in conneclion with the constellation 
Taurus. The average naked eye can easily distinguish six stars 
within it, but under favorable conditions ten, eleven, twelve, or more 
stars can be counted. With the telescope, over a hundred stars are 
seen. 

The clusters represented in Figs. 90 and 91 are good examples of 
their classes. The first is globular and contains several tliousand 
small stars. The second is a cluster of about 200 stars, of magni- 
tudes varying from the ninth to the thirteenth aud fourteenth, in 
•which the brighter stars are scattered. 




-Globular Cluster, 



Fig. 91 —Compressed Cluster, 



Clusters are probably subject to central powers or forces. This waa 
seen by Sir William Herschbl in 1789. He says: 

"Not only were ?w^w(^ nebulae and clusters formed by central 
powers, but likewise every cluster of stars or nebula that shows a 
gradual condensation or increasing brightness toward a centre. 
This theory of central power is fully established on grounds of ob- 
servation wiiich cannot be overturned. 

"Clusters can be found of 10 diameter with a certain degree of 
compression and stars of a certain magnitude, and smaller clusters 
of 4', 3', or 2' in diameter, with smaller stars and greater compression, 
and so on through resolvable nebulae by imperceptible steps, to th§ 



EEBULuS AND CLUSTERS. 309 

smallest and faintest [and most distant] nebulae. Other clusters there 
are, which lead to the belief that cither they are more compressed or 
are composed of larger stars. Spherical clusters are probably not 
more ditferent in size among themselves than different individuals of 
plants of the same species. As it has been shown that the spherical 
figure of a cluster of stars is owing to central powers, it follows that 
those clusters which, cceterv^ paribus, are the most complete in this 
figure must have been the longest exposed to the action of these 
causes. 

"The maturity of a sidereal sj'stem may thus be judged from the 
disposition of the component parts. 

"Though Ave cannot see any individual nebula pass through all 
its stages of life, we can select particular ones in each peculiar 
stage," and thus obtain a single view of their entire course of de- 
velopment. 

SPECTEA of NEBTJL.E AND CLUSTERS, AND FIXED STARS. 

In 1864, five years after the invention of the spectroscope, the 
exaniination of the spectra of the nebulae led to the discovery that 
while the spectra of stars were invariably continuous and crossed with 
dark lines similar to those of the solar spectrum, those of many ne- 
bulae were discontinuous, showing these bodies to be composed of 
glowing gas. 

The spectrum of most clusters is continuous, indicating that the 
individual stars are truly stellar in their nature. In a few cases, 
however, clusters are composed of a mixture of nebulosity (usually 
near their centre) and of stars, and the spectrum in such cases is 
compound in its nature, so as to indicate radiation both by gaseous 
and solid matter. 

Spectra of Fixed Stars. 

Stellar spectra are found to be, in the main, similar to the solar 
spectrum; i.e., composed of a continuous band of the prismatic col- 
ors, across which dark lines or bands were laid, the latter being fixed 
in position. These results show the fixed stars to resemble our own 
sun in general constitution, and to be composed of an incandescent 
nucleus surrounded by a gaseous and absorptive atmosphere of 
lower temperature. Tiiis atmosphere around many stars is different 
in constitution from that of the sun, as is shown by the different posi- 
tion and intensity of the various black lines and bands which are due 
to the absorptive action of the atmospheres of the stars, 



310 ASTRONOMY. 

It is probable that the hotter a star is the more simple a spectrum 
it has; for the brig:litest, and therefore probably the hottest stars, 
such as Sirius, give spectra showing only very thick hydrogen lines 
and a few very thin metallic lines, while the cooler stars, such as 
our sun, are shown by their spectra to contain a much larger num- 
ber of metallic elements than stars of the type of Sirius, but no 
non-metallic elements (oxygen possibly excepted). The coolest 
stars give band spectra characteristic of compounds of metallic 
with non-metallic elements, and of the non metallic elements un- 
combined. 

Motion of Stars in the Line of Sight. 

Spectroscopic observations of stars not only give information in 
regard to their chemical and physical constitution, but have been 
applied so as to determine approximately the velocity in kilometres 
per second with which the stars are approaching to or recedmg from 
the earth along the line joining earth and star. The theory of such a 
determination is briefly as follows: 

In the solar spectrum we find a group of dark lines, as a, b, c, 
which always maintain their relative position. From laboratory 
experiments, we can show that the three bright lines of incandescent 
hydrogen (for example) have always the same relative position as 
the solar dark lines a, b, c. From this it is inferred that the solar 
dark lines are due to the presence of hydrogen in its absorptive 
atmosphere. 

Now, suppose that in a stellar spectrum we find three dark lines 
a', b', c', whose relative position is exactly the same as that of the 
solar lines a, b, c. Not only is their relative position the same, but 
the characters of the lines tlieraselves, so far as the fainter spectrum 
of the star will allow us to determine them, are also similar; that is, 
a' and a, b' and b, c' and c are alike as to thickness, blackness, nebu- 
losity of edges, etc. etc. From this it is inferred that the star really 
contains in its atmosphere the substance whose existence has been 
shown in the sun. 

If we contrive an apparatus by which the stellar spectrum is seen 
in the lower half, say, of the eyepiece of the spectroscope, while 
the spectrum of hydrogen is seen just ab<.ve it, we find in some 
cases this remarka])le phenomenon. The three dark stellar lines, 
a' , b', c', instead of being exact Ij^ coincident with the three hydrogen 
lines a, b, c, are seen to be all thrown to one side or the other by a 
like amount; that is, the whole group a' , b' , c' , wiiile preserving its 
relative distai^ces the sanie as those of the comparison group a, b, c, 



^^BUL.^ AND CLtrsTEHS. 



Sll 



is shifted toward either the violet or red end of the spectrum by a 
small yet measurable amount. Repeated experiments by different 
instruments and observers show always a shifting in the same direc- 
tion and of like amount. The figure shows the shifting of the F 
line in the spectrum of Sirius, compared with one fixed line of 
hydrogen. 

This displacement of the 
spectral lines is to be ac- 
counted for by a motion of 
the star toward or from the 
earth. It is shown in Phy- 
sics that if the source of 
the light which gives the 
spectrum a, h', d is mov- 
ing away from the earth, 
this group will be shifted 
toward the red end of the 
spectrum ; if toward the 
eartli, then the whole group 
will be shifted toward the 
blue end. The amount of 
this shifting is a function of 
the velocity of recession or 
approach, and this velocity 
in miles per second can be calculated from the measured displace- 
ment. This has been done for many stars. The results agree well, 
when the difficult nature of the research is considered. The rates of 
motion vary from insensible amounts to 100 kilometres per second; 
and in some cases agree remarkably with the velocities computed 
from the proper motions and probable parallaxes. 




Fig. 92.— F Line in Spectrum op Sirius. 



CHAPTER V. 
MOTIONS AND DISTANCES OF THE STARS. 

Propee Motions. 

We have already stated that, to the unaided yisioii, the 
fixed stars appear to preserve the same relative position in 
the heavens through many centuries, so that if the an- 
cient astronomei's could again see them, they could hardly 
detect the slightest change in their arrangement. But 
accurate measurements have shown that there are slow 
changes in the positions of the brighter stars, consisting in 
a motion forward in a straight line and Avith uniform 
velocity. These motions are, for the most part, so slow 
that it would require thousands of years for the change of 
position to be perceptible to the unaided eye. They are 
called proper motions, since they are peculiar to the star 
itself. 

In general, the proper motions even of the brightest 
stars are only a fraction of a second in a year, so that 
thousands of years would be required for them to 
change their place in any striking degree, and hundreds 
of thousands to make a complete revolution around the 
heavens. 

Proper Motion of the Sun. 

It is a priori evident that stars, in general, must have 
proper motions, when once we admit the universality of 



MOTIONS AND DISTANCES OF THE STARS. 313 

gravitation. That any fixed star should be entirely at 
rest would require that the attractions on all sides of it 
should be exactly balanced. Any change in the position 
of this star would break up this balance, and thus, in gen- 
eral, it follows that stars must be in motion, since all of 
them cannot occupy such a critical position as has to be 
assumed. 

If but one fixed star is in motion, this affects all the 
rest, and we cannot doubt but that every star, our sun 
included, is in motion by amounts which vary from small 
to great. If the sun alone had a motion, and the other 
stars were at rest, the consequence of this would be tliat 
all the fixed stars would appear to be retreating en masse 
from that point in the sky toward which we were moving. 
Those nearest us would move more rapidly, those more 
distant less so. And in the same way, the stars from 
which the solar system was receding would seem to be 
approaching each other. If the stars, instead of being 
quite at rest, as just supposed, had motions proper to 
themselves, then we should have a double complexity. 
They would still appear to an observer in the solar system 
to have motions. One part of these motions would be 
truly proper to the stars, and one part would be due to the 
advance of the sun itself in space. 

Observations can show us only the resnltanf of these 
two motions. It is for reasoning to separate this resultant 
into its two components. At first the question is to deter- 
mine whether the results of observation indicate any solar 
motion at all. If there is none, the proper motions of 
stars will be directed along all possible lines. If the sun 
does truly move, then there will be a general agreement in 
the resultant motions of the stars near the ends of the line 



§14 AsmONOMf. 

along which it moves, while those at the sides, so to speak, 
will show comparatively less systematic effect. It is as if 
one were riding in the rear of a railway train and Avatching 
the rails over which it has Just passed. As we recede from 
any point, the rails at that point seem to come nearer and 
nearer together. 

If we were passing through a forest, we should see the 
trunks of the trees from which we were going apparently 
come nearer and nearer together, while those on the sides 
of us would remain at their constant distance, and those in 
front would grow further and further apart. 

These phenomena, which occur in a case where we are 
sensible of our own motion, serve to show how we may 
deduce a motion, otherwise unknown, from the appear- 
ances which are presented by the stars in space. 

In this way, acting upon suggestions which had been 
thrown out previously to his own time, Herschel demon- 
started that the sun, together with all its system, was mov- 
ing through space in an unknown and majestic orbit of its 
own. The centre round which this motion is directed 
cannot yet be assigned. We can only determine the point 
in the heavens toward which our course is directed — ** the 
apex of solar motion." 

A number of astronomers have since investigated this 
motion with a view of determining the exact point in the 
heavens toward which the sun is moving. Their results 
differ slightly, but the points toward which the sun is 
moving all fall in the constellation Hercules. The amount 
of the motion is such that if the sun were viewed at right 
angles to the direction of motion from an average star 
of the first magnitude, it would appear to move about one 
third of a second per year. 



MOTIONS AND DISTANCES OF THE STARS 315 

Distances of the Fixed Stars. 

The ancient astronomers supposed all the fixed stars to 
be situated at a short distance outside of the orbit of the 
planet Saturn, then the outermost known planet. The 
idea was prevalent that Nature would not waste space by 
leaving a great region beyond Saturn entirely empty. 

When CoPERKicus announced the theory that the sun 
was at rest and the earth in motion around it, the problem 
of the distance of the stars acquired a new interest. It was 
evident that if the earth described an annual orbit, then 
the stars would appear in the course of a year to oscillate 
back and forth in corresponding orbits, unless they were 
so immensely distant that these oscillations were too small 
to be seen. The apparent oscillation of Saturn pro- 
duced in this way was described in Part I. It amounts to 
some 6° on each side of the mean position. These oscilla- 
tions were, in fact, those wliich the ancients represented 
by the motion of the planet around a small epicycle. But 
no such oscillation had ever been detected in a fixed star. 
This fact seemed to present an almost insuperable difficulty 
in the reception of the Copernican system. Very natural- 
ly, therefore, as the instruments of observation were from 
time to time improved, this apparent annual oscillation of 
the stars was ardently sought for. 

The problem is identical with that of the annual parallax 
of the fixed stars, which has been already described. This 
parallax of a heavenly body is the angle which the mean 
distance of the earth from the sun subtends when seen 
from the body. The distance of the body from the sun is 
inversely as the parallax (nearly). Thus the mean distance 
of Satur7i being 9.5, its annual parallax exceeds 6°, while 



816 ASmOKOMY. 

that of Neptune, which is three times as far, is about 2^. 
It was very evident, without telescopic observation, that 
the stars could not have a parallax of one half a degree. 
They must therefore be at least twelve times as far as 
Saturn if the Copernican system were true. 

When the telescope was applied to measurement, a con- 
tinually increasing accuracy began to be gained by the 
improvement of the instruments. Yet for several genera- 
tions the parallax of the fixed stars eluded measurement. 
Very often indeed did observers think they had detected 
a parallax in some of the brighter stars, but their succes- 
sors, on repeating their measures with better instruments, 
and investigating their methods anew, found their conclu- 
sions erroneous. Early in the present century it became 
certain that even the brighter stars had not, in general, a 
parallax as great as 1", and thus it became certain that they 
must lie at a greater distance than 200,000 times that 
which separates the earth from the sun. 

Success in actually measuring the parallax of the stars 
was at length obtained almost simultaneously by two as- 
tronomers, Bessel of Konigsberg and STRUVE'of Dorpat. 
Bessel selected 61 Cygni for observation, in August, 1837. 
The result of two or three years of observation was that 
this star had a parallax of 0".35, or about one third of a 
second. This would make its distance from the sun nearly 
600,000 astronomical units. The reality of this parallax 
has been well-established by subsequent investigators, only 
it has been shown to be a little larger, and therefore the 
star a little nearer than Bessel supposed. The most j)rob- 
able parallax is now found to be 0".51, corresponding to a 
distance of 400,000 radii of the earth's orbit. 

The distances of the stars are sometimes expressed by 



MOTIONS AND DISTANCES OF THE STAMS. 317 

the time required for light to pass from them to our sys- 
tem. The velocity of light is, it will be remembered, about 
300,000 kilometres per second, or such as to pass from the 
sun to the earth in 8 minutes 18 seconds. 

The time required for light to reach the earth from some 
of the stars, of which the parallax has been measured, is as 
follows : 



Star. 


Years. 


Star. 


Years. 


a Centauri .... 

61 Cvani 


3-5 

6-7 

6-3 

(5.9 

9-4 

10. 5 

11.9 

13.1 

16-7 

17-9 


70 Oplduchi 

I Ursce Majoru 

Arcturvs 


19.1 
243 


21,185 Lelaude 


254 
35. 1 


// CassiopeicB 

84 firoombrido'G 


1830 Groom bridge.. 
Polnvis . . . 


35.9 
42.4 


21,258 Leiande 

17.415 Oeltzeu 


3077 Bradley 

85 Pegafii 

a Aurigce 


46. 1 
64-5 
70-1 


/y IjVVCB 


d Di'ciconis 


129 1 









CHAI>TER VI. 
CONSTRUCTION OF THE HEAVENS. 

The visible uniyei'se, as revealed to us by the telescope, is 
a collection of many millions of stars and of several thou- 
sand nebulae. It is sometimes called the stellar or sidereal 
system, and sometimes, as already remarked, the stellar 
universe. The most far-reaching question with which 
astronomy has to deal is that of the form and magnitude 
of this system, and the arrangement of the stars which 
compose it. 

It was once supposed that the stars were arranged on the 
same general plan as the bodies of the solar system, being 
divided up into great numbers of groups or clusters, while 
all the stars of each group revolved in regular orbits round 
the centre of the group. AH the groups were supposed to 
revolve around some great common centre, which ' was 
therefore the centre of the visible universe. 

But there is no proof that this view is correct. We have 
already seen that a great many stars are collected into clus- 
ters, but there is no evidence that the stars of these 
clusters revolve in regular orbits, or that the clusters them- 
selves have any regular motion around a common centre. 

The first astronomer to make a careful study of the arrangement 
of the stars with a view to learn the structure of the heavens was Sir 
William Herschel. 

Herschel's method of study was founded on a mode of observa- 



CONSTRUCTION OF THE HEAVENS. 



319 



tion which he called star-gauging. It consisted in pointing a power- 
ful telescope toward various parts of the heavens and ascertaining by 
actual count how thick the stars were in each region, llis 20-foot 
reflector was provided with such an eye piece that, in looking into 
it, he would see a portion of the heavens about 15' in diameter. A 
circle of this size on the celestial sphere has about one quarter the 
apparent surface of the sun, or of the full moon. On pointing the 
telescope in any direction, a greater or less number of stars were 
nearly always visible. These were counted, and the direction in 
which the telescope pointed was noted. Gauges of this kind were 
made in all parts of the sky at which he could point his instrument, 
and the results were tabulated in the order of right ascension. 

The following is an extract from the gauges, and gives the average 
number of stars in each fiekl at the points noted in ligiit ascension 
and north-polar distance: 







N. P. D. 






N. P. D. 


R. 


A.. 


9:i<» to 94°. 
No. of Stars. 


R A. 




78° to 80°. 
No. of Stars. 


h. 


m. 




h.] 


m.] 




15 


10 


9.4 


11 


6 


8.1 


15 


47 


10.6 


12 


44 


4.6 


16 


25 


13.6 


12 


49 


3.9 


16 


37 


18.6 


14 


30 


3.6 



In this small table, it is plain that a different law of clustering or 
of distribution obtains in the two regions. 

The number of these stars in certain portions is very great. For 
example, in the Milky Way this number was as great as 116,000 stars 
in a quarter of an hour in some cases. 

Herschel supposed at first tiiat he completely resolved the whole 
Milk}^ Way into small stars. This conclusion he subsequently modi- 
fied. He says: 

" It is very probable that the great stratum called the ]\[ilky Way is 
that in which the sun is placed, though perhaps not in the very cen- 
tre of its thickness. 

" We gather this from the appearance of the Galaxy, which seems 
to encompass the whole heavens, as it certainly must do if the sun is 
within it. For, suppose a number of stars arranged between two 
parallel planes, indefinitely extended every way, but at a given con- 
siderable distance from each other, and calling this a sidereal stratum, 
Un Q^Q placed ^omew^ere withia it will sge all tjie stars in lUe direc- 



320 



ASTRONOMY. 



lion of the planes of the stratum projected into a great circle, which 
will appear lucid on account of the accumulation of the stars, while 













*%^ 









Fig. 93.— Herschkl's Theory of the Stellar System. 

the rest of the heavens, at the sides, will only seem to be scattered 
over with constellations, mo|-e ov less crowded, according to the di§- 



CONSTRUCTION OF THE HEAVENS. 321 

tance of the planes, or number of stars contained in tlic lliickness or 
sides of the stratum." 

Thus in Herschel's figure an eye at S within the stratum ah will 
see the stars in the direction of its length ab, or height cd, with all 
those in the intermediate situations, projected into the lucid circle 
A C B D, while those in the sides mv, nw, will be seen scattered over 
the remaining part of the heavens MVNW. 

"If the eye were placed somewhere without the stratum, at no 
very great distance, the appearance of the stars within it would 
assume the form of one of the smaller circles of the sphere, which 
would be more or less contracted according to the distance of the 
eye; and if this distance were exceedingly increased, the whole 
stratum might at last be drawn together into a lucid spot of any 
shape, according to the length, breadth, and height of the stratum. 

" Suppose that a smaller stratum pq should branch out from the 
former in a certain direction, and that it also is contained between 
two parallel planes, so that the eye is contained within the great 
stratum somewhere before the separation, and not far from the place 
where the strata are still united. Then this second stratum will not 
be projected into a bright circle like the former, but it will be seen 
as a lucid branch proceeding from the first, and returning into it 
again at a distance less than a semicircle. 

"In Ihe figure the stars in the small stratum p 5' will be projected 
into a bright arc PER P, which, after its separation from tiie circle 
CB D, unites with it again at P. 

"If the bounding surfaces are not parallel planes, but irregularly 
curved surfaces, analogous appearances must result." 

The Milky Way, as we see it with the naked eye, presents the 
aspect which has been just accounted for. in its general appearance 
of a girdle around the heavens and in its bifurcation at a certain 
point, and Herschel's explanation of this appearance, as just given, 
has never been seriously questioned. One doubtful point remains: 
are the stars in Fig. 93 scattered all through the space S — abpdl 
or are they near its bounding planes, or clustered in any way within 
this space so as to produce the same result to the eye as if uniformly 
distributed ? 

Herschel assumed that they were nearly equably arranged all 
through tlie space in question. He only examined one other arrange- 
ment — viz., that of a ring of stars surrounding the sun — and he pro- 
nounced against such an arrangement, for the reason that there is 
absolutely nothing in the size or brilliancy of the sun to cause us to 
suppose it to be tiie centre of such a gigantic system. No reason ex- 
cept its importance to us personally can be alleged for such a sup- 



322 ASTROyOMY. 

position. By the assumptions of Fig. 93. each star will have its 
own appearance of a galaxy or milky way, which will vary accord- 
ing to the situation of the star. 

Such an explanation will account for the general appearances of 
the Milky Way and of the rest of the sky. supposing the stars equally or 
nearly equally distributed in space. On this supposition, the system 
must be deeper where the stars appear more numerous. 



CHAPTER VII. 
COSMOGOXY. 

A THEORY of the operations by which the universe re- 
ceived its present form and arrangement is called Cosmog- 
ony. This subject does not treat of the origin of matter, 
but only of its transformations. 

Three systems of Cosmogony have prevailed among 
thinking men at different times: 

(1) That the universe had no origin, but existed from 
eternity in the form in which we now see it. This was the 
view of the ancient philosophers. 

(2) That it was created in its present shape in a mo- 
ment, out of nothing. This view is based on the literal 
sense of the words of the Old Testament. 

(3) That it came into its present form through an ar- 
rangement of materials Avhich were before ''without form 
and void." This may be called the evolution theory. It 
is to be noticed that no attempt is made to explain the 
origin of the primitive matter. 

The last is the idea which has prevailed, and it receives 
many striking confirmations from the scientific discoveries 
of modern times. The latter seem to show beyond all rea- 
sonable doubt that the universe could not always have 
existed in its present form and under its present condi- 
tions ; that there was a time when the materials composing 
it were masses of glowing vapor, and that there will be a 



324 ASTRONOMY. 

time when the present state of things will cease. The ex- 
planation of the processes throngh which this occurs is 
sometimes called the nehular hypothesis. It was first pro- 
pounded by the philosophers Swedenborg, Kakt, and 
Laplace, and, although since greatly modified in detail, 
their views have in the main been retained until the 
present time. 

We shall begin its consideration by a statement of the 
various facts which appear to show that the earth and 
planets, as well as the sun, were once a fiery mass. 

The first of these facts is the gradual but uniform in- 
crease of temperature as we descend into the interior of 
the earth. Wherever mines have been dug or wells sunk 
to a great depth, the temperature increases as we go down- 
ward at the rate of about one degree centigrade to every 30 
metres, or one degree Fahrenheit to every 50 feet. The 
rate differs in different places, but the general average k 
near this. The conclusion which we draw from this may 
not at first sight be obvious, because it may seem that the 
earth might always have shown this same increase of tem- 
perature. But there are several results which a little 
thouglit will make clear, although their complete establish- 
ment requires the use of the higher mathematics. 

The first result is that the increase of temperature can- 
not be merely superficial, but must extend to a great 
depth, probably even to the centre of the earth. If it did 
not so extend, the heat would have all been lost long ages 
ago by conduction to the interior and by radiation from 
the surface. It is certain tliat the earth has not received 
any great supply of heat from outside since the earliest 
geological ages, because such an accession of heat at the 
earth's surface woiild have destroyed all life, and even 



COSMOGONY. 325 

melted all the rocks. Therefore, whateyer heat there is 
in the interior of the earth must have been there from be- 
fore the commencement of life on the globe, and remained 
through all geological ages. 

The interior of the earth being hotter than its surface, 
and hotter than the space around it, must be losing heat. 
We know by the most familiar observation that if any ob- 
ject is hot inside, the heat will work its way through to the 
surface by the process of conduction. Therefore, since the 
earth is a great deal hotter at the depth of 30 metres than 
it is at the surface, heat must be continually coming to the 
surface. On reaching the surface, it must be radiated off 
into space, else the surface would have long ago become 
as hot as the interior. Moreover, this loss of heat must 
have been going on since the beginning, or at least since 
a time wlien the surface was as hot as the interior. Thus, if 
we reckon backward in time, we find that there must have 
been more and more heat in the earth the further back 
we go, so that we must finally reach back to a time when 
it was so hot as to be molten, and then again to a time 
when it was so hot as to be a mass of fiery vapor. 

The second fact is that we find the sun to be cooling off 
like the earth, only at an incomparably more rapid rate. 
The sun is constantly radiating heat into space, and, so far 
as we can ascertain, receiving none back again. A small 
portion of this heat reaches the earth, and on this portion 
depends the existence of life and motion on the earth's sur- 
face. The quantity of heat which strikes the earth is only 
about ^-o-oWiroo-oTr ^^ ^^^^^ which the sun radiates. This 
fraction expresses the ratio of the apparent surface of the 
earth, as seen from the sun, to that of the Avhole celestial 
sphere. 



326 ASTRONOMY. 

Since the sun is losing heat at this rate, it must have had 
more heat yesterday than it lias to-day ; more two days ago 
than it had yesterday, and so on. Thus calculating back- 
ward, we find that the further we go back into time the 
hotter the sun must have been. Since we know that heat 
expands all bodies, it follows that the sun must have been 
larger in past ages than it is now, and we can trace back 
this increase in size without limit. Thus we are led to the 
conclusion that there must have been a time when the sun 
filled up the space now occupied by the planets, and must 
have been a very rare mass of glowing vapor. The plan- 
ets could not then have existed separately, but must have 
formed a part of this mass of vapor. The latter was there- 
fore the material out of which the solar system was 
formed. 

The same process may be continued into the future. 
Since the sun by its radiation is constantly losing heat, it 
must grow cooler and cooler as ages advance, and must 
finally radiate so little heat that life and motion can no 
longer exist on our globe. 

The third fact is that the revolutions of all the planets 
around the sun take place in the same direction and in 
nearly the same plane. We have here a similarity amongst 
the different bodies of the solar system, which must have 
had an adequate cause, and the only cause which has ever 
been assigned is found in the nebular hypothesis. This 
hypothesis supposes that the sun and planets were once 
a great mass of vapor, as large as or larger than the present 
solar system, revolving on its axis in the same plane in 
which the planets now revolve. 

The fourth fact is seen in the existence of nebulae. The 
spectroscope shows these bodies to be masses of glowing 



COSMOGONY. 827 

vapor. We thus actually see matter in the celestial spaces 
under the very form in which the nebular hypothesis sup- 
poses the matter of our solar system to have once existed. 
Since these masses of vapor are so hot as to radiate light 
and heat through the immense distance which separates us 
from them, they must be gradually cooling off. This cool- 
ing must at length reach a point when they will cease to 
be vaporous and condense into objects like stars and 
planets. We know that every star in the heavens radiates 
heat as our sun does. In the case of the brighter stars the 
heat radiated has been made sensible in the foci of our 
telescopes by means of the thermo-multiplier. All the 
stars must, like the sun, be radiating heat into space. 

A fifth fact is afforded by the physical constitution of 
the planets Jupitei' and Saturn. The telescopic examina- 
tion of these planets shows that changes on their surfaces 
are constantly going on with a rapidity and violence to 
which nothing on the surface of our earth can compare. 
Such operations can be kept up only through the agency of 
heat or some equivalent form of energy. But at the dis- 
tance of Jupiter and Saturn the rays of the sun are entirely 
insufficient to produce changes so violent. We are there- 
fore led to infer that Jupiter and Saturn must be hot 
bodies, and must therefore be cooling off like the sun, 
stars, and earth. 

We are thus led to the general conclusion that, so far 
as our knowledge extends, nearly all the bodies of the 
universe are hot, and are cooling off by radiating their 
heat into space. 

The idea that the heat radiated by the sun and stars may 
in some way be collected and returned to them by the 
operation of known natural laws is equally untenable. It 



328 ASTRONOMY. 

is a fundamental principle of the laws of heat that " the 
latter can never pass from a cooler to a warmer body," and 
that a body can never grow warm or acquire heat in a space 
that is cooler than the body is itself. All diiferences of 
temperature tend to equalize themselves, and the only 
state of things to which the universe can tend, under its 
present laws, is one in which all space and all the bodies con- 
tained in space are at a uniform temperature, and then all 
motion and change of temperature, and hence the condi- 
tions of vitality, must cease. And then all such life as ours 
must cease also unless sustained by entirely new methods. 

The general result drawn from all these laws and facts 
is, that there was once a time when all the bodies of the 
universe formed either a single mass or a number of masses 
of fiery vapor, having slight motions in various parts, and 
different degrees of density in different regions. A grad- 
ual condensation around the centres of greatest density then 
went on in consequence of the cooling and the mutual at- 
traction of the parts, and thus arose a great number of 
nebulous masses. One of these masses formed tire ma- 
terial out of which the sun and planets are supposed to 
have been formed. It was probably at first nearly glob- 
ular, of nearly equal density throughout, and endowed 
with a very slow rotation in the direction in which the 
planets now move. As it cooled oZ, it grew smaller and 
smaller, and its velocity of rotation increased in rapidity. 

The rotating mass we have described must have had an axis 
around which it rotated, and therefore an equator defined 
as being everywhere 90° from this axis. In consequence 
of the increase in the velocity of rotation, the centrifugal 
force would also be increased as the mass grew smaller. 
This force varies as the radius of the circle described by 



COSMOGONY. 329 

any particle multiplied by the square of its angular velocity. 
Hence when the masses, being reduced to half the radius, 
rotated four times as fast, the centrifugal force at the equa- 
tor would be increased ix4% or eight times. The grayi- 
tation of the mass at the surface, oeiug iuyersely as the 
square of the distance from the centre, or of the radius, 
would be increased four times. Therefore as the masses 
continue to contract, the centrifugal force increases at a 
more rapid rate than the central attraction. A time would 
therefore come when they would balance each other at the 
equator of the mass. The mass would then cease to con- 
tract at the equator, but at the poles there would be no 
centrifugal force, and the gravitation of the mass would 
grower stronger and stronger. In consequence the mass 
would at length assume the form of a lens or disk very thin 
in pro2)ortion to its extent. The denser portions of this 
lens would gradually be drawn toward the centre, and there 
more or less solidified by the process of cooling. A point 
would at length be reached, when solid particles would begin 
to be formed throughout the whole disk. These would grad- 
ually condense around each other and form a single ])lai]et, or 
they might break up into small masses and form a group of 
planets. As the motion of rotation would not be altered 
by these processes of condensation, these planets won hi all 
be rotating around the central part of the mass, which is 
supposed to have condensed into the sun. 

It is supposed that at first these planetary masses, being 
very hot, were composed of a central mass of those sub- 
stances which condensed at a very high temperature, sur- 
rounded by the vnpors of those substances whicli were 
more volatile. We know, for instance, that it takes a much 
higher temperature to reduce lime and platinum to vapor 



330 ASTRONOMY. 

tlum it does to reduce iron, zinc, or magnesium. There- 
fore, in tlie original planets, the limes and earths would 
condense first, while many other metals would still be in 
a state of vapor. The planetary masses would each bo 
affected by a rotation increasing in rapidity as they grew 
smaller, and would at length form masses of melted metals 
and Ta2")ors in the same way as the larger mass out of which 
the sun and planets were formed. These masses would 
then condense into a planet, with satellites revolving 
around it, just as the original mass condensed into sun and 
planets. 

At first the planets would be so hot as to be in a molten 
condition, each of them probably shining like the sun. 
They would, however, slowly cool off by the radiation of 
heat from their surfaces. So long as they remained liquid, 
the surface, as fast as it grew cool, would sink into the in- 
terior on account of its greater specific gravity, and its 
place would be taken by hotter material rising from the 
interior to the surface, there to cool off in its turn. There 
would, in fact, be a motion something like that which 
occurs when a pot of cold water is set upon the fire to boil. 
Whenever a mass of water at the bottom of the pot is 
lieated, it rises to the surface, and the cool water moves 
down to take its place. Thus, on the whole, so long as 
the planet remained liquid, it would cool off equally 
throughout its whole mass, owing to the constant motion 
from the centre to the circumference and back again. A 
time would at length arrive when many of the earths and 
metals would begin to solidify. At first the solid particles 
would be carried up and down with the liquid. A time 
would finally arrive when they would become so large 
and numerous, and the liquid part of the general mass 



COSMOGONY. 331 

become so viscid, that the motion would be obstructed. 
The planet would then begin to solidify. Two views 
have been entertained respecting the process of solidifica- 
tion. 

According to one view, the whole surface of the planet 
would solidify into a continuous crust, as ice forms over a 
pond in cold weather, while the interior was still in a 
molten state. The interior liquid could then no longer 
come to the surface to cool off, and could lose no heat 
except what was conducted through this crust. Hence 
the subsequent cooling would be much slower, and the 
globe would long remain a mass of lava, covered over by 
a comparatively thin solid crust like that on which we 
live. 

The other view is that, when the cooling attained a cer- 
tain stage, the central portion of the globe would be 
solidified by the enormous pressure of the superincumbent 
portions, while the exterior was still fluid, and that thus 
the solidification would take place from the centre out- 
ward. 

It is still an unsettled question whether the earth is now 
solid to its centre, or whether it is a great globe of molten 
matter with a comparatively thin crust. Astr^li^mers and 
physicists incline to the former view ; geologists to the lat- 
ter one. Whichever view may be correct, it appears cer- 
tain that there are great lakes of lava in the interior from 
which volcanoes are fed. 

It must be understood that the nebular hypothesis, as we 
have explained it, is not a perfectly established scientific 
theory, but only a philosophical conclusion founded on the 
widest study of nature, and pointed to by many otherwise 
disconnected facts. The widest generalization associated 



382 ASTMONOMY. 

witli it is that, so farjis avc cun sec, the universe is not self- 
sustaining, but is a kind of organism wliicli, like all other 
organisms we know of, must come to an end in consequence 
of those very laws of action which keep it going. It must 
liave had a beginning within a certain number of years 
which we cannot yet calculate with certaint}', but which 
cannot much exceed 20,000,000, and it must end in a chaos 
of cold, dead globes at a calculable time in the future, 
when the sun and stars shall have radiated away all their 
heat, unless it is re-created by the action of forces of which 
we at present know nothing. 



THE END. 



INDEX. 



B^" This index is intended to point out the subjects treated in tlic 
work, and furtiier, lo give references to the pages where technical 
terms are detined or explained. 



Aberration-constant, value of, 
178. 

Aberration of light, 174. 

Achromatic telescope described, 
63. 

Adams's work on perturbations 
of Uranus, 256. 

Airy's determination of the den- 
sity of the earth, 148. 

Algol (variable star), 296. 

Altitude of a star defined, 18. 

Angles, 3. 

Annular eclipses of the sun, 135. 

Apparent place of a star, 16. 

Apparent time, 45. 

Aristarciius determines the so- 
lar parallax, 165. 

Asteroids defined, 191. 

Asteroids, number of, 225 in 
1882, 238. 

Astronomical instruments (in 
general), 60. 

Astronomy (defined), 1. 

Atmosphere of the moon, 231. 

Atmospheres of ihe planets. See 
Mercury, Venus, etc. 

Axis of the earth defined, 21. 

Azimuth defined, 19. 



Bessel's parallax of 61 Cygni 

(1837), 315. 
Binary stars, 302. 
Bode's law staled, 193. 
Bond's discovery of the dusky 

ring of Saturn, 1850, 250. 
Bou yard's theory of Uranus, 

256. 
Bradley discovers aberration in 

1729, 176. 
Calendars, how formed, 182. 
Cassini discovers four satellites 

of Saturn (1684-1671), £52. 
Catalogues of stars, general ac- 
count, 79. 
Celestial sphere, -14. 
Centre of gravity of the solar 

system, 194. 
Chronology, 180. 
Chronometers, 68. 
Clarke's elements of the earth, 

152. 
Clocks, 68. 
Clusters of stars. 308. 
Comets, general account, 274. 
Comets' orbits, 277 
Comets' tails, repulsive force, 

277. 



884 



INDEX. 



Comets, their physical constitu- 
tion, 276. 

Comets, their spectra, 377. 

Conjunction (of a planet witli 
the sun) defined, 97. 

Constellations, 288. 

Construction of the heavens, 317. 

Co-ordinates of a star defined, 
19, 37. 

Copernicus, 103. 

Correction of a clock defined, 69. 

Cosmogony, 322. 

Corona, its spectrum. 216. 

Day, how subdivided into hours, 
etc., 187. 

Days, mean solar and solar, 46. 

Declination of a star defined, 41. 

Distance of the fixed stars, 314. 

Distribution of the stars, 818. 

Diurnal motion, 21, 22. 

Dominical letter, 186. 

DoNATi's comet (1858), 281. 

Double (and multiple) stars, 301. 

Earth (the), general account of, 
142. 

Earth's density, 142. 

Earth's dimensions, 151. 

Earth's mass, 142. 

Eclipses of the moon, 131. 

Eclipses of the sun and moon, 
129. 

Eclipses of the sun, explanation, 
132. 

Eclipses of the sun, physical 
phenomena, 212. 

Eclipses, their recurrence, 136. 

Ecliptic defined, 84. 

Elements of the orbits of the ma- 
jor planets, 198. 

Elongation (of a planet) defined, 
97.^ 



Encke's comet, 283. 

Encke's value of the solar paral- 
lax, 8". 578, 166. 

Epicycles, their theory, 102. 

Equation of time, 188, 

Equator (celestial) defined, 21. 

Equatorial telescope, description 
of, 74. 

Equinoxes, 87. 

Eye-pieces of telescopes, 62. 

Fabritius observes solar spots 
(1611), 207. 

Figure of the earth, 148. 

Future of the solar system, 332. 

Galaxy, or milky way, 319. 

Galileo observes solar spots 
(1611), 207. 

Galileo's discovery of satellites 
of Jupiter (1610), 240. 

Galle first observes Neptune 
(1846), 259. 

Geodetic surveys, 150. 

Golden number, 184. 

Gravitation extends to the stars, 
303. 

Gravitation resides in each par- 
ticle of matter, 119. 

Gravitation, terrestrial (its laws), 
146. 

Greek alphabet, 11. 

Gregorian calendar, 185. 

Halley predicts the return of a 
comet (1682), 279. 

Hali/s discovery of satellites of 
Mars, 235. 

Hansen's value of the solar par- 
allax, 8". 92. 166. 

Herschel (W.) discovers two 
satellites of Saturn (1789), 252. 

Herschel (W.) discovers two 
satellites of Uranus (1787), 254. 



INDEX. 



335 



Herschel (W.) discovers Uranus 
(1781), 253. 

Herschel's catalogues of nebu- 
la3, 305. 

Herschel's star-gauges, 318. 

Herschel (W.) states that the 
solar system is in motion (1783), 
312. 

Herschel's (W.) views on the 
nature of nebulae, 305. 

Hlpparchus discovers preces- 
sion, 153. 

Hooke's drawings of Mars 
(1666), 234. 

Horizon (celestial — sensible) of 
an observer defined, 17, 20, 

Hour-angle of a star defined, 39. 

HuGGiNs' determination of mo- 
tion of stars in line of sight, 
310. 

HuGGiNS first observes the spec- 
tra of nebulae (1864). 309. 

HuYGHENS discovers a satellite 
of Saturn (1655), 252. 

HuTGHENS discovers laws of 
central forces, 116. 

HuYGHENs' explanation of the 
appearances of Saturn's rings 
(1655), 248. 

Inferior planets defined, 99. 

Intramercurial planets, 226. 

Janssen first observes solar pro- 
minences in daylight, 213. 

Julian year, 184. 

Jupiter, general account, 240. 

Jupiter's rotation-time, 242. 

Jupiter's satellites, 243, 

Kant's nebular hypothesis, 323. 

Kepler's laws enunciated, 109. 

Laplace's nebular hypothesis, 
323. 



Laplace's investigation of the 
constitution of Saturn's rings, 
252. 

Laplace's relations between the 
mean motions of Jupiter's satel- 
lites, 243. 

Lassell discovers Neptune's sat- 
ellite (1847), 260. 

Lassell discovers two satellites 
of Uranus (1847), 254. 

Latitude (geocentric — geogra- 
phic) of a place on the earth de- 
fined, 8, 31, 41, 152. 

Latitude of a point on the earth 
is measured by the elevation of 
the pole, 31. 

Latitudes and longitudes (celes- 
tial) defined, 95. 

Latitudes (terrestrial), how deter- 
mined, 53. 

Le Verrier computes the orbit 
of metoric shower, 271. 

Le Yerrier's researches on the 
theory of Mercury, 226. 

Le Terrier's work on perturba- 
tions of Uranus, 257. 

Light-gathering power of an ob- 
ject-glass, 63. 

Light-ratio (of stars) is about 2.5, 
295. 

Line of collimation of a telescope, 
71. 

Local time, 47. 

Lockyer's discovery of a spec- 
troscopic method, 216. 

Longitude of a place, 9, 10. 

Longitude of a place on the 
earth (how determined), 50, 52. 

Longitudes (celestial) defined, 
95. 

Lucid stars defined, 289. 



336 



INDEX. 



Lunar phases, nodes, etc. See 
Moon's phases, nodes, etc. 

Magnifying power of an eye- 
piece, 65. 

Major planets defined, 191. 

Mars, physical description, 233. 

Mars, rotation, 234. 

Mars's satellites discovered by 
Hall (1877), 235. 

Maskelyne determines the den- 
sity of the earth, 145. 

Mass of the sun in relation to 
masses of planets, 167. 

Mean solar time defined, 45. 

Mercury's atmosphere, 244. 

Mercury, its apparent motions, 
221. 

Meridian (celestial) defined, 27. 

Meridian circle, 72. 

Meridians (terrestrial) defined, 
27. 

Metonic cycle, 183. 

Meteoric showers, 269. 

Meteors and comets, their re- 
lation, 271. 

Meteors, their cause, 265. 

Milky Way, 289. 

Milky Way, its general shape ac- 
cording to Herschel, 319. 

Minor planets defined, 191. 

Minor planets, general account, 
237. 

Mira Ceti (variable star), 296. 

Months, different kinds. 182. 

Moon, general account, 228. 

Moon's light -^^j^ists of the sun, 
232. 

Moon's phases, 123. 

Moon's parallax, 161, 

Moon's surface, does it change? 
233. 



Motion of stars in the line of 

sight, 310. 
Nadir of an observer defined, 18. 
Nautical almanac described, 79. 
Nebulte and clusters in general, 

304. 
Nebulae, their spectra, 309. 
Nebular hypothesis stated, 322. 
Neptune, discovery of, by Le 

Vekrier and i?LDAMS (1846), 

256. 
Neptune, general account, 256. 
Neptune's satellite, 260. 
New stars, 298. 
Newton (I.) calculates orbit of 

comet of 1680, 280. 
Newton (I.), Laws of Force, 

115. 
Objectives, or object-glasses, 60. 
Obliquity of the ecliptic, 91. 
Occultations of stars by the moon 

(or planets), 140. 
Olbers's hypothesis of the ori- 
gin of asteroids, 239. 
Olbers predicts the return of a 

meteoric shower, 269. 
Old style (in dates), 185. 
Opposition (of a planet to the 

sun) defined, 85. 
Parallax (annual) defined, 58. 
Parallax (horizontal) detined, 56. 
Parallax (in general) defined, 50. 
Parallax of the sun, 161. 
Parallax of the stars, general ac- 
count, 314. 
Parallel sphere detined, 28. 
Peuumbraoft lit earth's or moon's 

shadow, 131. 
Photosphere of the sun, 201. 
PiAzzi discovers the first asteroid 

(1801), 237. 



INDEX. 



387 



Planets, their relative size exhib- 
ited, 191. 

Planetary nebulae defined, 306. 

Planets; seven bodies so called 
by the ancients, 81. 

Planets, their apparent and real 
motions, 96. 

Planets, their physical constitu- 
tioD, 261. 

Poles of the celestial sphere de- 
fined, 31. 

Pouillet's measures of solar ra- 
diation, 205. 

Practical astronomy (defined), 78. 

Precession of the equinoxes, 
153. 

Prime vertical of an observer de- 
fined, 19. 

Problem of three bodies, 119. 

Proper motions oi stars, 312. 

Proper motion of the sun, 312. 

Ptolemy determines the solar 
parallax, 166. 

Radiant point of meteors, 270. 

Radius vector, 107. 

Reflectiog telescopes, 66. 

Refracting telescopes, 60. 

Refraction of light in the atmos- 
phere, 169. 

Resisting medium in space, 281. 

Reticle of a transit instrument, 
71. 

Retrogradations of the planets 
explained, 100, 

Right ascension of a star defined, 
40. 

Right ascensions of stars, how 
determined by observation, 72. 

Right sphere defined, 29. 

RoEMER discovers that light 
moves progressively, 175. 



Rosse's measure of the moon's 

heat, 232. 
Saros (the), 140. 
Saturn, general account, 246. 
Saturn's rings, 248. 
Saturn's satellites, 252. 
Seasons (the), 92. 
Secchi, on solar temperature, 

206. 
Semidiameters (apparent) of ce- 
lestial objects, 59. 
Sextant, 76. 

Sidereal time explained, 43. 
Sidereal year, 153. 
Signs of the Zodiac, 90. 
Solar corona, etc. See Sun, 
Solar corona, extent of, 213. 
Solar cycle, 185. 
Solar heat, its amount, 204. 
Solar motion in space, 312. 
Solar parallax, history of attempts 

to determine it, 165. 
Solar parallax probably about 

8" -81, 168. 
Solar prominences are gaseous, 

213. 
Solar system, description, 190. 
Solar system, its future, 220. 
Solar temperature, 206. 
Solstices, 94. 
Spectrum of Solar prominences, 

214. 
Spectrum of Solar corona, 216. 
Spectrum of Mercury and Venus, 

262. 
Spectrum of Nebulae and Clus-. 

ters, 309. 
Spectrum of fixed Stars, 309. 
Spectrum as indicating motions 

of stars, 310. 
Star-clusters, 308. 







338 



INDEX. 



Star-gauges of Herschel, 318. 

Stars had special names 3000 B.C., 
291. 

Star-magnitudes, 290. 

Stars of various magnitudes, how 
distributed, 294. 

Stars — parallax and distance, 
314. 

Stars seen by the naked eye 
about 2000, 291. 

Stars, their proper motions, 312. 

Stars, their spectra, 310. 

Struye's (W.) parallax of alpha 
Lyrce (1838), 315. 

Summer solstice, 88. 

Sun's apparent path, 86. 

Sun's constitution, 217. 

Sun's (the) existence cannot be in- 
definitely long, 220, 325. 

Sun's mass over 700 times that of 
the planets, 194. 

Sun, physical description, 200. 

Sun'^8 proper motion, 312. 

Sun's rotation-time about 25 
days, 200. 

Sun-spots and faculse, 200, 206. 

Sun-spots are confined to certain 
parts of the disk, 208. 

Sun-spots, their nature, 209. 

Sun-spots, their periodicity, 211. 

Superior planets (defined), 99. 

Swedenborg's nebular hypothe- 
sis, 323. 

Swift's supposed discovery of 
Yulcan, 226. 

Symbols used in astronomy, 11. 

Telescopes, their advantages, 66. 

Telescopes (reflecting), 66. 

Telescopes (refracting), 60. 



Tempel's comet, its relation to 

November meteors, 272. 
Temporary stars, 298. 
Tides, 126. 
Total solar eclipses, description 

of, 212. 
Transit instrument, 70. 
Transits of Mercury and Venus, 

225. 
Transits of Venus, 163. 
Triangulation, 150. 
Tropical year, 154. 
Twilight, 172. 
Tycho Brahe observes new star 

of 1572, 299. 
Universal gravitation discovered 

by Newton, 121. 
Universal gravitation treated, 

113. 
Uranus, general account, 253. 
Variable and temporary stars. 

general account, 296. 
Variable stars, theories of, 299. 
Velocity of light, 179. 
Venus's atmosphere, 224. 
Venus, its apparent motions, 221. 
Vernal equinox, 87. 
Vulcan, 226. 
Watson's supposed discovery of 

Vulcan, 226. 
Weight of a body defined, 143. 
Wilson's theory of sun-spots, 

210. 
Winter solstice, 89. 
Years, different kinds, 183. 
Zenith defined, 17. 
Zodiac, 90. 
Zodiacal light, 272. 



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